Re:
Buy whichever one they want, Barbie, action man, whatever. They'll ride them more if the bikes appeal to them. The bikes will be garbage, but they grow out of them so quickly it won't matter.
I tried to talk mine into Islabikes, which are probably the best kids bikes available, short cranks, well thought out spec for kids etc but they weren't interested, so we ended up with a 12" giant, followed by a 16" Raleigh, then a 20" Dawes and lastly a 24" dawes. The one thing they all had in common was that they are so damn heavy.
Thankfully they are now big enough to ride full size mountain bikes, albeit with 14 and 16" frames respectively. Retro of course.. rebuilt konas, a 98 cindercone and a 99 explosif. And as they grow I can just move the kit onto bigger frames.