Start with a Trooper (Republic side) or Bounty Hunter (Imperial side); preferably go Vanguard (Trooper tank/DPS advanced class) or Powertech (BH tank/DPS advanced class), although that's less important.
Almost everybody starts with one of the Jedi classes, because, c'mon, they're Jedi. (Or sometimes Sith, same reason.) Their basic attacks are melee, though, so you have a little bit more to worry about while you're figuring out the basics of the game. Smuggler and Agent are ranged, but they preferably fight from cover (although that's less important now than it used to be--it used to be that most of their attacks
only worked from cover), so again, a little bit more to figure out right at the start. Troopers and Bounty Hunters are straight-up ranged fighters, and they're the only classes that wear heavy armor from the start, so they're a little bit more survivable.
Keep playing that class at least to the end of the first planet (Ord Mantell or Hutta) and preferably to the end of the second (Coruscant or Dromund Kaas); at that point, if you like them, keep playing them; if you don't like them, switch to something else. By then, you'll have a solid feel of the basic mechanics of the game, and learning a new class will just be learning that class, not learning how the entire game works at the same time.
As Free-to-Play (aka F2P) you don't gain experience quite as quickly as a subscriber, so go into the map (default key M) and click the "Show Exploration Missions" checkbox at the top right. That will both give you more opportunities to gain experience and show you a little bit more of the game world. One of the best things about TOR is that the world (or worlds, really
) is very well-developed, and doing side missions shows you a little more about it. That checkbox might be on by default for new players; I'm not sure. Anyway, after you've played the game for a while (certainly after you've gotten your first characters through the storyline on each side) you'll want to turn that off to streamline the game somewhat, but for the first run-through I recommend keeping it on.
Enjoy TOR!