charmstot,
I think the advice being discussed on here is productive, but I recommend you try my way. Instead of trying to figure out which is most basic, I find it easier to figure out which is least acidic (this is equivalent, but sometimes easier to think in terms of this).
For this problem, if you do it this way, it is obviously the one with the methyl group attached to the amine group, since it has the least amount of substituents to stabilize the positive charge (if the N lost a proton).
Great discussion though everyone!!!