You're right in that it's not really possible to screw up, at least at the earlier levels. TOR is a lot like WoW in how it plays so you should already have a good grasp on the mechanics and the interface.
Best advice is just take your time, mobs can swarm you pretty easilly if you're not careful and harder enemies like elites are a lot more common than WoW so you need to keep an eye out and watch your back.
Another bit of advice is to take the time to do side quests, they're a bit monotonous at times but it's worth it for the xp and level advantage when you come back to your Class Quests as some of them can be a pain.
Aside from those, there isn't much else I can think of that you wouldn't already know from WoW. Choose professions early and level them as you go, Flashpoints (Dungeons) are a great way to get good gear and xp, you never really need to waste money on purchasing anything from vendors aside from perhaps medpacks and stims if you want the extra buffs.
Otherwise enjoy the game, Bioware's always been good at telling stories and while some class stories are definitely better than others, they're all worth at least a look.