What is your skill level distribution? Are you all the same? Is one of you really good and the other 2 okay? Not judging, it's just that 2v2 can get real boring real fast when 1 player is significantly better or worse than the other 3, makes it impossible to balance the game...so, you'll probably want to find someone that compliments your skill set...
What time during the week are you looking to play? Weekdays? Weekends? Night? Afternoon?
For now, you may want to consider these games:
2v2v2 - each of you is coupled with an AI...if you have a particularly strong or weak player, you can adjust the difficulty of their AI ally accordingly...
1v2v1 - this is an interesting game mode...it sounds really dumb at first, but it actually can be a lot of fun...it has the dynamics of a FFA, but is better balanced if you have one weak human player (who would be coupled with the AI)...