Balance bike or 12" Bike & Gender Neutral

We'd like to get either a balance bike or a 12" bike for our daughter turning 3 next week. She is 38" tall. It MUST be gender neutral since she'll probably only ride it this summer/fall and it will go to her brother (her sister has a 16" bike she'll get next summer). So...
1) Balance bike or 12" bike?
2) If balance bike, which balance bike do we buy?
3) If 12" bike, do 12" gender neutral bikes exist? It seriously seems like the only options are soooo girly or totally boy!