I love my Canon SD630.
http://www.usa.canon.com/consumer/controller?act=ModelDetailAct&fcategoryid=145&modelid=12956
Width and height is equal to a credit card, depth is obviously bigger. This thing is teeny but packs a high quality punch.
I had a crappy Sony 2MP camera for about 5 years. It took the worst pictures ever, but I spent about $160 on it in 2002.
For under $200, I don't think you'll be happy with the results. If you are happy, you'll probably outgrow it quickly.
I strongly recommend any Canon camera, especially the PowerShot models. There is an SD430 that is quite a good camera. It'd probably do you quite well. I know people that have had their PowerShot for a long time and are still 100% satisfied with it.