The full list that Rebels have access to is in the OP. Most notable? As above, I'm partial to three X-wings as my squadron builds. That's definitely not all that works, though. Some ships that show up in tournaments a lot (which is a good idea to see what's good/notable, if not a good idea to see what you should play [which is whatever you want, **** the meta]):
Han Solo - YT1300. This guy is arguably one of the best ships in the game, due to his ability and combining him with certain upgrade cards (Gunner, Predator, Engine Upgrade) and the 360 degree turret all YTs have.. A Han loaded down with a bunch of upgrades is known colloquially as a "Fat Han". I don't actually own one of these because I hate flying big ships.
Dash Rendar - YT2400. Also ridiculously good, due to the Outrider title that lets him put cannons on a turret and give no ****s about anything in the way. Cannons are secondary weapons, so they have the handy effect of taking away extra defense bonuses from long range shots. Stupidly mobile with the right upgrades, colloquially called "Epic Dash". Also comes with a bunch of cool upgrades. I don't catually own one of these either, for the same reason.
Corran Horn - E-wing. Can shoot twice in a turn, in exchange for not shooting the next turn. The only E-wing pilot worth using. Pairs very well with either Fat Han or Epic Dash as part of a two-ship squadron list. For a long time, two ship lists were the dominant part of the entire meta. Recent releases have changed that pretty significantly, but they were good for a reason, and they're still good even if they're not outright the best anymore.
Keyan Farlander - B-wing. Can spend stress (removing it) as a focus token while attacking. Stress normally sucks really hard, so that's a pretty awesome ability. Held back a little bit by the pilot skill in a world full of aces (PS 7, in an odd middle ground in the game where you're higher than generic pilots (and paying for it) but not high enough to consistently beat aces unless you grab Veteran Instincts, which makes it more difficult to get stress tokens through that upgrade slot). Pilot ability generally makes up for it, and the B-wing's maneuver dial has a good deal of red to help out with that. B-wings are also pretty tanky, with five shield points and three hull points.
Blue Squadron Pilot - B-wing. Generic, PS 2 B-wing. Cheap, durable, painful, not particularly dodgy, restricted dial. Four of these guys and a Z-95 make up probably the best, most realiable jousting list in the game, at the cost of limited maneuver options to keep guns on target after the merge.
Jake Farrel - A-wing. When assigned a focus token, he can perform a boost or barrel roll, making him the single most mobile small ship on the entire Rebel side. Same PS as Keyan, but A-wings get to take two of them with the upgrades in Rebel Aces (which is where you get Jake in the first place) which makes it a bit easier to keep him competitive with other aces.
Green Squadron Pilot - A-Wing. Relatively cheap generic fighter that is pretty good at staying out of arcs. Comes with an Elite Pilot Talent (the lowest pilot skill ship in the game with an EPT at PS 3), and can get another with upgrades out of Rebel Aces. Along with Jake, arguably needs Autothrusters (found in the Star Viper) to truly come into its own against ships with turrets.
Wedge Antilles - X-wing. One of exactly five pilots in the game with native PS 9 (along with Han Solo, Darth Vader, Soontir Fel, and Talonbane Cobra). Expensive, and X-wings have serious difficulty in modern games due to lack of after-maneuver reposition options like barrel roll and boost. Still an awesome pilot, and will lay down the goddamn hurt on whatever you point him at. Helped by...
Wes Jansen - X-wing. Not as high PS as Wedge (PS 8), but with a pilot ability arguably better. When he shoots at someone, they lose a token, either a focus, evade, or target lock. You pick. Really, really, really good at setting up shots for the rest of your group. Put Veteran Instincts on him to get him to PS 10 and unleash him on a target you want to focus fire against.
Poe Dameron - T-70 X-wing. Sublime. T-70s kick serious ass, and Poe's ability is basically Luke's ability, with a few of the little details changed. High skill (PS 8) and a boost action means he's maneuverable as hell, and adding upgrades like BB-8 (Astromech) and Push the Limit means that he can pull of maneuvers and actions in such an order that he can effectively get 5-speed banks and 7-speed forward maneuvers, which are normally impossible. Everybody else has to do those reposition options after the maneuver, but Poe has the unique ability to do them both before he actually moves.
Gold Squadron Pilot - Y-wing. Low cost, PS 2 pilot that is suddenly all the rage because Twin Laser Turrets kick ass, and you can fit four of these guys into a tournament list with them. Sturdy, not very shooty (without turrets), not very dodgy, not very zippy. This is why they're cheap.
Bandit Squadron Pilot - Z-95. If the Y-wing is cheap, the Z-95 is dirt. A Gold Squad Y-wing costs 18 points, a Bandit Squad Z-95 costs 12, equivalent to a TIE Fighter. You can fit eight of them in a tournament list, which is expensive (in real dollars) and has some serious trouble with arc dodgers like Soontir (big in the meta) and Vader (also big). Point and shoot.
Miranda Doni - K-wing. The highest skill offering for the K-wing (PS 8), her ability is impressive. Once per round, Miranda may choose to either roll one fewer attack die in order to regenerate a shield (there are exactly four ways to regenerate shields in X-wing. All four of them are for Rebels only, two of them are Astromechs [and therefore restricted to X-wings, Y-wings, and E-wings only], one of them is a crew upgrade [and therefore limited to the YT-1300, YT-2400, HWK-290, and B-wing (with upgrades)] with a downside.), or spend a shield to roll an additional attack die. Obviously that's pretty sweet and flexible, and Miranda herself sees a lot of play next to Corran or a Fat Han/Epic Dash in a two ship build.
Jan Ors - HWK-290. Hawks are support ships, plain and simple. Jan is high skill (PS 8), but you don't take her for that, you take her for the pilot ability. If a friendly ship is nearby , you can take a stress token on Jan in order to have that ship roll an additional attack die. Attack dice are huge in this game. More of them is almost always great, especially if it doesn't take actions to do. Downsides: Fragile, slow, really really ****ty on offense.
There are probably a bunch more of them that I missed, but those are the ones I see on the field most often on the Rebel side.