We all know how frustrating it is to try to join a game and someone already has your color, and while picking a different color, the game auto-starts because someone else joined while you were picking. I think that in the setting, that there should be a way to set a secondary and third color.

I second this

Please add this feature Fizzer

This is not a bad idea to be honest, however, maybe a setting to choose a free color if yours is not available instead of setting a secondary, as this could still cause problems, you should create a uservoice on this

Uservoice.

If in a small game only one open seat remains and you have to choose an other color first, somebody else sometimes get it. Alternative colors would partially prevent this situation.

There's a uservoice entry for this already, vote there:
http://warlight.uservoice.com/forums/77051-warlight-features/suggestions/2382010-secondary-colors