Some thoughts, and I'll just apologize now for the cold water I'm likely going to be pouring all over everything.
First up, gaming on a laptop is a big no-no. Unless you want to be playing games that are 5-6 years old, just forget about it. Even 5-6 year old games will probably be pushing it a bit.
Second, regardless of brand, I would recommend avoiding sub-$1000 laptops. They're typically going to be garbage, and you're likely going to outgrow it very quickly.
Third, is that HP in general is crap IMO. Better than Acer, but only just. Especially on their low end systems, the level of quality control seems to be little to non-existent. Apple is probably #1 in quality, but you will pay for it. Dell usually provides what I find to be the best mix of price and quality. They're neither the best nor the cheapest, but they're the best for the money. Again, IMO. Toshiba is another option for good quality for the price.
Fourth, laptops and school sound like a great idea, but they're really not. If you use the thing in class, it won't be long before you're spending most of your time talking to friends or doing something other than listening to the lecture. Better to do this the old fashioned way, so to speak. Have a desktop in your dorm or apartment, and that's it. Take notes by hand in class, and then transcribe them on the computer later if you want. Desktops will give you more gaming options as well.
Fifth, you can't really get a good feel for a laptop in a store. Until you've had the thing for a week or two, you'll never really know for sure. It takes time to learn some of the various quirks of a system, and there are things you can't easily do in a store that you will do later, and may be disappointed.
If you want my advice, look for a desktop, and preferably one that's not an HP/Compaq or Acer/Gateway/eMachines brand. Don't even take so much as a smartphone with you to class, or you'll be screwing around on that rather than listen to the lecture, and then you'll fail your classes. Since these days all lectures seem to be are professors reading a power point presentation, you can just print those off in a lab before class, then take notes in the margins.
If you must get a laptop, I'd hold off until you have a little bit more of a budget so you don't wind up with a piece of crap. I tell people to avoid any desktop $500 and under. Laptops don't have the same upgrade options as desktops, so it's even more important to buy quality from the beginning. You should also check with your school. A lot of them have deals with a couple of vendors for students. It's at least worth looking into and comparing to Costco. And for our east cost readers, Costco is a warehouse club like Sams Club or BJs.
I am thinking of buying a new laptop in the $600 range. This would be my first laptop so I would have little experience. I don?t need anything, just a typical student laptop. Internet browsing, video chat, Youtube a few games and documents. I am currently looking at the HP g62t laptop. http://www.ubergizmo.com/15/archives/2010/02/hp_g62t_is_powerful_and_looks_sleek.html I tried it once at a Costco and I really like it. But I was wondering if you guys might have any more suggestions?