Try Dota 2, it's free and basicly created a videogame genere.
That's kinda wrong.
DotA was the truly first MOBA game, while who really gave that name to this sub-genre of RTS was Riot Games when they already launched League o Legends. Today MOBA is a hyped game genre, where you can see a race from everywhere to get a good MOBA game into the same mainstream as LoL(DotA 2, Smite and Heroes of the Storm).
The best of all in DotA 2 is its tutorial. It's really simple, but give you all the mechanics of the game. Although you may want single player games, always remember that you can play with bots locally.