Also knowing which classes are good is a HUGE factor in arena. Rogue, Paladin, Mage, Druid.
Yeah, pretty much in that order, too (best to worst). And you should never play Priest or Hunter, and Warlock and Shaman are kind of weak too.
Well, you CAN play any class in arena and get at least 4-5 wins even with the weak ones. You just need a lot of experience to be successful with those. "Weak" arena classes are characterized by their "zero-tempo" hero powers (among other things), i.e. their powers do not change the current board state.
Priest can be an exception with the right minions already in play.
Shaman's hero power is just terrible and his good cards are mostly rare and epic and don't combo very well (it's probably the worst class overall and honestly needs a rework).
Warlock and Hunter, however, do have several very powerful common cards. With those classes you might need to draft a little more low-curve (choose more minions costing 2 or 3 mana than usual) and only use their hero powers in the late game. Then you should be able to get a decent number of wins with them easily.
Warrior, similarly, has got some good common cards including weapons which he needs to establish an early-game lead but he needs more support for the late game like taunts and heals (because he took so much damage from attacking with weapons). If your opponent is a Paladin or Mage and also has a strong late game, you'll probably lose with Warrior. And you encounter a lot of Paladins and Mages in arena so I don't recommend picking Warrior.
When you are an experienced player, you should just pick whatever class you feel like in arena. Unless your draft is terrible, you should always be able to get 4 wins or so.