The things I looked for within my budget:
--resolution: I needed at least 7 megapixels so that I could make large prints, even when cropping sections of the original image;
--lens: couldn't afford dSLR with separate lenses, so had to look for decent built-in lenses; optical zoom is the key element (digital zoom does NOT cut it) and went with 10x.
I regret not getting a model with a hot shoe, as built-in flashes just don't work well for what I do.
For my next camera, I'm requiring a hot shoe and at least 9 megapixels. If I can swing a dSLR, then I'll do that, otherwise I'm looking at 12x optical zoom on built-in lenses.