Protoss - Zealot
Zerg - Zergling
Terran - Marine
The game is just a beta at the moment but they are updating the game all the time. You learn to play very quickly, it's not complicated at all.
Here are some screens from the game.
This is how your stats screen look like.
And here is the score from a fight with "Steve" that i won.
I think if we give the game some time it will be a very good browser-based game.
Play - Starcraft Ascension
SCLegacy - Source