I hate HP/Compaq with a passion myself.
I have a toshiba.. lots went wrong with it at first.. had to replace some stuff, I didn't do it through them, just did it myself.. since then its run like a charm for quite a while (5 years or so).
I wouldn't reccomend gateway.. I hear they are mainly POS...
I've heard a lot of bad things about Vios
I'd go with dell.. they tend to undersell their cheaper systems.. they end up loosing money on the cheaper systems because they expect to sucker you into buying something just a bit better.
On the fringe.. Lenovo, fujitsu, and panasonic seem to make solid notebooks.. though i'm not sure if any of them have anything cheap.
I reccomend lightweight and battery over proccessor power. You might want to chip in some extra and get a tablet if your going to take notes on it in class.. because drawing diagrams with a keyboard is hard.