I like Canon's. In that price range, the Canon Powershot.
http://www.steves-digicams.com/best_cameras.html (scroll down to "4 Megapixel" and "Entry Level")
I'd like to add that megapixels here is not the main thing to be looking at. All that pretty much means is that you can have images at larger resolutions. 4megapixels is really all you need on consumer digicams.
Edit: In the price range, brand isn't that big a deal anymore - pick one that feels comfortable in your hand and where the controls and their locations feel ok to you.
In terms of the jpg compression thing - I kinda doubt it'll be too big a deal for most of the things you might use it for, as long as the image resolution is high enough. Just always keep the original and work from a copy or crop, if that makes sense, thus preserving the original jpg's quality every time you edit it.