If we accept all the Star Wars films as the same canon (as it seems we must) then a lot that happens in the original films has to be reinterpreted in the light of the prequels. As we now know, the rebel Alliance was founded by Yoda, Obi-Wan Kenobi and Bail Organa. What can readily be deduced is that their first recruit, who soon became their top field agent, was R2-D2.
Consider: at the end of Revenge of the Sith, Bail Organa orders 3PO's memory wiped but not R2's. He would not make the distinction casually. Both droids know that Yoda and Obi-Wan are alive and are plotting sedition with the Senator from Alderaan. They know that Amidala survived long enough to have twins and could easily deduce where they went. However, it can be assumed that R2 makes an impassioned speech to the effect that he is far more use to them with his mind intact: he has observed Palpatine and Anakin at close quarters for many years, knows much that is useful and is one of the galaxy's top experts at hacking into other people's systems. Also he can lie through his teeth with a straight face. Organa, in immediate need of espionage resources, agrees.
For the next 20 years, as far as C3PO knows, he is the property of Captain Antilles, doing protocol duties on a diplomatic transport. He is vaguely aware of the existence of Princess Leia but he doesn't know much about her. Wherever 3PO goes, being as loud and obvious as he always is, his unobtrusive little counterpart goes with him. 3PO is R2's front man. Wherever they land, R2 is passing messages between rebel sympathisers and sizing up governments as potential rebel recruits - both by personal contact and by hacking into their networks. He passes his recommendations on to Organa.
Yoda is out of the picture by this stage, using the Force-infused swamps of Dagobah to hide himself from Vader and the Emperor. Or something. He is meditating on the future and keeping in touch with Obi-Wan via the ghost of Qui-Gon Jin, which as comm systems go has the virtue of being untappable. Obi-Wan, on Tattoine, keeps in touch with Bail Organa and the other Rebel leaders by courier, of which more later.
As Star Wars opens, R2 is rushing the Death Star plans to the Rebellion. That’s R2, not Leia. The plans are always in R2. What Leia puts into him in the early scene is only her own holographic message to Kenobi. Leia's own mission, as she says in that holographic message, is to pick up Obi-Wan and take him to Alderaan. Or so she thinks. Actually, her father just wants her to meet Kenobi, which up to this point she never has. There's a reason for that.
Obi-Wan has spent the last 20 years in the Tattoine desert, keeping watch over Luke Skywalker and trying to decide on one of the three available options: A) If Luke shows no significant access to the Force, then leave him alone in obscurity B) If Luke shows real Force ability, then consider recruiting him as a Jedi. The rebellion needs Jedi and it needs them now.But, if Luke shows any signs of turning out like his father, then: C) sneak into his house one fine night and chop his head off. With great regret but it'll save a lot of trouble later on.
Knowing this to be the case, Bail Organa (perhaps at the insistence of his wife) has found excuses not to send Leia to Ben for assessment of Jedi potential, largely for fear of option C. To be fair to all concerned, Leia has shown no overt signs of a link to the Force. Luke on the other hand has. In his home-built hotrod aircraft, with no formal fighter pilot training and no decent instrumentation, Luke can regularly score centre-hits on two-metre targets in complex zero-altitude maneouvres. Until he attends the briefing on Yavin, Luke has no way of knowing that hardened combat pilots would consider that nearly impossible. To him it's easy. Obi-Wan, who saw Anakin's performance in the Pod Race, is nervous.
Much of Obi-Wan's behaviour in this film, and Yoda's in the next, can best be understood if they are frankly scared to death of what Luke might become. (Ben is also scared that he himself will make all the same mistakes he made with Anakin.) Now, with the existence of the rebellion at stake, Bail Organa has finally told Leia to go see Obi-Wan and has sent her along with R2. The original plan would then be for Obi-Wan (with optional Luke and/or Leia in tow) to leave his exile and take the Death Star plans to Yavin, where they can be put to use. R2 (with Leia if Ben doesn't want to take her) would then carry on to Alderaan to maintain the cover story. The original plan does not survive contact with a large Imperial Star Destroyer.
R2 and 3PO bail out in an escape pod. Landing in vaguely the right area of Tattoine, R2's first priority is transport. He arranges to be captured by a group of Jawas and, once on board their vehicle, he makes a deal with them (possibly using emergency funds stored elsewhere on the planet) to take him where he wants to go. The Jawas refuse to go directly to Kenobi for fear of marauding Sandpeople but they agree to R2's second request : transport to the farm of Owen Lars. They even get to keep the purchase price if they can sell R2 and 3PO there. R2 and the Jawas shake on it and they go through with the plan.
Seeing 3PO fail to recognise the farm where he worked for 10 miserable years gives R2 a moment's amusement but, as soon as opportunity presents itself, he makes a break for it and heads for Obi-Wan. Luke and 3PO follow, which may or may not have been part of the plan.
On first seeing R2, Obi-Wan has a twinkle in his eye and calls him "my little friend". Well, he is. However, when Luke wakes up and says that R2 claimed to be owned by an Obi-Wan Kenobi, Ben blandly says "I don't seem to remember ever owning a droid." Ben has in fact owned several but the remark is aimed at R2 and translates as "You keep quiet. I'm not about to tell him everything just yet." Obi-Wan thinks fast and tells Luke a version of his past that does not involve a father who became a dark lord of the Sith. Ben wants to examine Luke a lot more closely before he risks telling him the real truth.
Although the Death Star plans need to get to Yavin as soon as possible, Obi-Wan has one more diversion to make first. If the Empire knows that Leia is a Rebel leader, then they also know about her father, so the whole Organa family may need immediate evacuation. Fortunately, before coming to Tattoine, R2 had already arranged transport, which is waiting at Mos Eisley under the command of the Rebellion's other chief field agent and espionage asset. Chewbacca.
Twenty years earlier, Chewbacca was second in command of the defence of his planet. He was there in the tactical conferences and there on the front lines and was a personal friend of Yoda's. So when he needed reliable people to join the embryonic Alliance, who else would Yoda turn to but his old friend from Kashykk? Given his background, it makes no sense that Chewbacca would spend the crucial years of the rebellion as the second-in-command to (sorry Han) a low-level smuggler. Unless it was his cover. In fact, Chewie is a top-line spy and flies what is in many ways the Rebellion's best ship.
The Millenium Falcon may look like a beat-up old freighter but it can outrun any Imperial ship in normal space or hyperspace, hang in a firefight with a Star Destroyer or outmaneouvre a dozen top-of-the-line TIE fighters. It's a remarkable feat of engineering and must have cost a colossal fortune to build. How does Han come to own a ship like that? Actually, he only thinks he does – the real owner is Chewie. Half-way through Revenge of the Sith, we see the Falcon landing at the Senate building on Coruscant. If it's the same ship (which of course it is) then it was the personal transport of one of the senatorial delegations - a much more likely source to commission its design. That delegation must have later joined the Rebellion and given it the use of the Falcon. In fact, if the delegation was the one from Kashykk, then the ship may have belonged to Chewbacca as early as Revenge of the Sith.
Han is Chewbacca's front man. It's much better, and safer for him, if he doesn't know what's really going on. Chewie used to work with Lando Calrissian in a similar way but Lando wanted to settle down, so Chewie arranged for him to lose the Falcon in a card game to Han Solo, an even better choice as a partner. Han and Chewie's working method is pretty much what we see in the cantina scene: Chewie make the contacts and sets up the deals, then turns them over to Han, who haggles over the price and gives the final yea or nay. This lets Chewbacca wander the seamy underside of the galaxy pretty much at will, making contacts, gathering and passing information with no-one was the wiser, especially not Han.
It was Chewie who persuaded Han to do business with Jabba the Hutt, so that they could make regular runs to Tattoine, where Chewie could pass messages between Kenobi and Organa. When R2's urgent message came through only days before, the only way for Chewie to get back to Tattoine in time was to make the "mistake" that forced Han to dump his cargo to avoid capture. As a down side, this led to Solo's getting a death mark out on him from Jabba the Hutt. Chewie was a bit upset about that but figured they weren't going to be dealing with Tattoine for much longer.
En route to Alderaan, R2 and Chewie play stop-motion chess. This is the latest in a series of games that they've played over the years in the back rooms of space stations and cantinas across the galaxy, but this is the first time they've done it in front of their respective straight men, so they put on a big show.
Then it all goes wrong again. Alderaan has been destroyed and the Falcon is captured and brought aboard the Death Star. Han, Luke and 3PO don't know just how much trouble they're in but Obi-Wan, R2 and Chewbacca know only too well. However, Obi-Wan has a plan and seems confident of pulling it off (but then Jedi always do). Soon afterwards, while Obi-Wan is away, R2 discovers that Leia is in the detention cells and shouts out that they have to rescue her, to which Chewie can only agree. If Vader learns that he has a daughter, then they're all in very deep trouble, so Chewie does his bit to persuade Han to go along with Luke's impromptu rescue plan.
The escape nearly works but then Vader himself turns up only yards away from both of his children, one of whom is leaking Force in all directions. Obi-Wan sees what is happening and stages a distraction by letting himself die and go into the Force while the others escape.
At this point, Chewbacca suddenly realises that he's been left in charge, not only of the Death Star Plans and the survival of the Rebellion (which would be responsibility enough) but of the secret son and daughter of Darth Vader. With the Organas and Kenobi all dead, only Chewie, R2 and Yoda know who Luke and Leia really are and only Obi-Wan had any idea where to find Yoda. Chewbacca is stressed out by his new responsibilities and R2 (who keeps making crude jokes about the whole affair) is being no help at all. Chewie's first problem is what is happening between Luke and Leia. With a psychic link they can feel but not understand, thrown together in a life-or-death escape, they are looking at each other with a sparky intensity that Chewie gradually recognises as Romantic Tension. He is no expert on human relationships but Chewie is fairly sure that that's Wrong, so he does the only thing he can think of under the circumstances - he throws Han at her. Han is not interested at first, but after a while he starts to warm to the idea with an intensity that gives Chewie new worries.
When they reach Yavin, Han opts to take the money and run and Chewie decides to go with him. Looked at in a cold light, it's for the good of the Rebellion. Even if Yavin is destroyed, there will be one agent who knows what's going on who can try to put something back together. Still, Chewie doesn't feel good about it and when Han decides to turn around and join the attack, the wookiee is all for it. With the Death Star destroyed, Han and Luke get medals but Chewie doesn't. Actually, Leia offers him one but the wookiee turns it down. He got one of those things from Yoda about twenty years ago, but there's no way he can tell her that.
As the film ends, the three founders of the Rebellion are all gone. Bail Organa is dead, Yoda is out of contact and the ghost of Obi-Wan Kenobi can only talk to other Jedi. (So that would be Yoda then.) Thus, the field leadership of the rebellion has just been turned over to the daughter of Darth Vader. Chewie is hoping that someone with an official rank greater than hers will reach Yavin soon, before he has to think really seriously about option C.