teshra: Everquest 2 meets your criteria and is still the best mmo I've played. Paladins, rogues, fighters, clerics, necromancers and then some classes are available to you. Elves, dwarves, gnomes, humans and then some races are available. ... There's also mercenaries you can hire in town to help you in dungeons or quests/adventuring in general if you can't find a group.
Note that most of this isn't free. Most races and classes need to be bought, and mercenaries are available only if you buy the Age of Discovery expansion. There are quite a few limitations to F2P, but if you upgrade from Bronze (free) to Silver, which costs $5 (or less, I'll explain in a moment), the game is quite playable, even if still limited. It's possible to play Bronze, and it's a good way to check out the game, but buying Silver is definitely worth it to get more bag slots, more character slots and fewer restrictions.
EQ2 is the game I played most after (the unfortunately dead) City of Heroes, and unfortunately I never got far into it. It's pretty easy these days to play it solo (it's
a lot easier than it was in 2005-6 which was the first time I played it) and the early levels are generally fun, but I find that after level 20 it's not that easy to find story content, and you fall on a lot of "I'm too lazy or afraid to do this myself, so do it for me" type of quests. Not that it's impossible, but it requires some work, and it's a turn-off for me.
Still, I think it's an enjoyable game, and if you decide to play it then I'd suggest waiting for a double or triple SC sale. That's Sony's virtual currency and buying it at a triple SC sale basically means that you're paying a third of the normal price for what you buy in the game. There are also game sales, which can mean that you can end up paying a sixth of the normal price if you buy at a triple SC sale and then buy items at 50% off.