Whether you get the 250GB over the 4GB depends on what deals you can get on bundles, and whether your kids are likely to want to install games to the hard drive or use Live to download demos, XBLA games, DLC etc.
You can use a USB stick to add storage space, as long as it passes the performance test done by the 360 (most decent brand name sticks should pass).
Also, take into consideration the space requirements for Kinect, especially as it'll be used in a bedroom. You need about 6 feet of space for 1 player games and 8 feet for 2 player. Some people on here have got it to work with less space than that, but I would assume that's the minimum you need as that's what's recommended by MS.