Brands dont really matter much anymore; Dell, HP, Gateway... I think they're all the same now and I'm an IT guy. Personally I'd go with Dell because I think they're a little cheaper than the others but watch out for add-ons. Since you don't want a small keyboard, go with a larger laptop. The smaller ones are usually more expensive and less powerful anyway. I think HP does make widescreen laptops with full keyboards and number pads, which is pretty nice. Depends on how mobile you'll be though since those are a bit cumbersome. If you're just moving around a room or building mostly, a big laptop is no big deal... but if you're lugging it all over campus every day, it would make more of a difference.
Get plenty of RAM and a big, fast HDD and you should be fine with speed.
EDIT: New Egg is a great way to go for finding excellent deals on laptops. Like I said, brands don't matter much and so long as you're not too concerned with warranties and support (most colleges offer this service free anyway) a generic laptop would do just fine. I think they sell a lot of Asus, Acer and Lenovo laptops at great prices, and even some higher end Toshiba's and Sony's for good deals.
If you're a battery, you're either working or you're dead....