Best digital camera under $250?

I need to buy a digital camera and am having trouble picking one. it needs to be under $250 US , I'd like minimum of 4 MP, has to be fast because I mostly take pics of my 2 year old who is always on the go, clarity is important not too much noise. I usually won't make larger than an 8x10. I guess size isn't too important, but the smaller the better. I need a good zoom, preferably optical. I have a Kodak EasyShare CX4300 which I hate although it does take nice pictures and is only a 3.2 MP. It's just really slow., I have a Kodak EasyShare z700 on layaway, but have heard from many that the flash is way too bright so I'm not too sure about that one although it does have 5x optical zoom. Any suggestions would be great.

You want a cheap ultra compact digital camera with long optical zoom? That's a really tall order. Here's a few options. There are trade offs to everyone of them though:
DiMAGE X50, only 2.8x zoom, older generation, very small.
DiMAGE Z20, bigger than compact, 8x zoom.
Panasonic DMC-FX8, only 3x zoom, but stylish.
Panasonic DMC-LZ1, older generation, small but not that small, probably a good choice if you can find it.
Nikon Coolpix P2, average in every way, not that small, but it's a new cheap model.
Nikon Coolpix L1, no view finder. LCD only, great zoom though.
Nikon Coolpix S1, older model, 3x zoom only

How about the fujifilm
FinePix A345
4.1 mega pixels
10.8 zoom
large, bright LSD

Any Cannon under $250....A75 is a good one.