I would have to say my favorite flavor is Mint Chocolate Chip. It's always been my favorite flavor as long as I can remember. I don't know why I like that one so much but I do.
Definitely vanilla. If it's two flavor then I prefer vanilla and chocolate, strawberry is fine too. To be fair I rarely find any ice cream flavor that I hate, I even eat durian flavored ice cream.
My all time--absolute--favorite ice cream flavor is Mint Chocolate Chip. I found it several years ago and fell in love with it at first bite (see what I did there). They even make those Klondike bars in the flavor which is great because it keeps us from gorging ourselves into tummy aches on ice cream (not that we would).