I think the usual advice it start with whatever ships you think are cool. Most ships are usable, and you'll have more fun flying things you like. If you want a bit more: the ships "loosely" fall into three strategic types. There are
Jousters,
Arc Dodgers, and
Turrets, and they form a kind of rock, paper, scissors dynamic.
Jousting is what it sounds like: your ships fly straight towards the enemy, trading shots, then do a u-turn (k-turn, in X-wing speak), and repeat. If you played an intro game then you probably already saw some jousting. Ships with a lot of hit-points, such as B-Wings, or swarms of cheap ships, such as Academy Pilot Tie Fighters tend to be best at jousting.
This video tutorial explains how to fly swarms in formation, to get the most out of them.
Arc Dodgers, are faster more manoeuvrable ships that rely on their agility and aerobatics to survive. They usually entail Ace pilots with a high Pilot Skill, fast ships with the Boost action (either natively or from the Engine Upgrade card), and some way of squeezing extra actions, usually the Push the Limit upgrade. Popular Arc Dodgers are Soontir Fel (Tie Interceptor) with Push the Limit, Darth Vader (Tie Advanced) with Engine Upgrade, and for the Rebels A-wings with Push the Limit. Arc Dodgers take a bit of practice to use, but they are probably the most fun ships to fly. If flown well they will run rings around Jousters. Other popular upgrades are things like Autothrusters and Stealth Device to make them more survivable, and things like Proton Rockets which get better on higher agility ships. I'd recommend playing some games with Soontir Fel and Push the Limit, to dip your toe into Arc Dodgers.
Turrets are self explanatory, they are ships with turret weapons that can fire 360. A lot of the large ships like the Millennium Falcon, YT-2400, Jumpmaster, etc... do turrets well, and also Y-Wings make good cheap turret upgrade platforms (for spamming lots of turrets). Turrets are annoying for Arc Dodgers because the arc is 360, but they can sometimes take advantage of weapon range to find blind spots. Jousters and Swarms will usually be able to trade blows with Turrets and simply out-gun them (at least point for point).