And I'm not going to get into that debate. But, here is some general advice from a non-techie consumer who has owned many different systems.
If you go the "other" route, I'd suggest an AMD processor over Intel. Go with the Athlon version, at least the 2200. I also prefer ATI graphics cards, but there are arguments both ways on this. Look for something in this area that complies with OpenGL 2.0 and DirectX 9.0. Use name-brand, not generic, memory, at least 512mb if you're going to run Windoze XP. There's only a slight difference in price, and while generic memory can often be just as good as the non-generic, you can also end up with a memory chip that dies on you fairly quickly. With your DVD drive, check some review sites and look for some commentary on the noise factor. A lot of cheap DVD drives are very, very noisy, which can be very annoying. There's a particular brand that techtv.com recommended some time back, but I can't remember it right now.
Wireless keyboards and mice are all the rage right now. Be aware that your battery can die on you in the midst of writing that term-paper that's due in two hours, and you're stuck. Also, a lot of wireless mice have a response-delay problem that can be irritating. Definitely go with an optical mouse, though. They're not much more expensive than ball-mice and are much better. I prefer Logitech mice and keyboards.
I'd also suggest going to a local company that puts together systems and doesn't necessarily have a name brand attached to it. My reason for this is simply one of service and flexibility. On many of those pre-built systems from Dell, Gateway, etc., you're going to end up with proprietary/third-party parts and/or software that you won't be happy with. I've heard horror stories about Gateway, and I have horror stories about HP.
After years of buying pre-built systems from name manufacturers and having some very bad experiences, I finally took the advice of my techie friends and went to a local merchant who built the systems himself. I made sure I found several that had been in business for awhile, and the system I settled on is the best system I have ever owned. I've done a lot of my own upgrades, i.e. installing new memory, graphics, sound, etc., and I've had no problems at all. You'll hear of a lot of problems from people upgrading "name brand" systems.
Go around to several local dealers and talk to them. Tell them what you think you want, listen to what they tell you, and compare. Ask about their service and warranty policies. Get a feel for whether you're talking to a salesperson or someone who actually knows the products by asking unusual questions you already know the answers to. (Read a computer magazine or some online review sites to get an idea on what kinds of questions to ask.
http://www.tomshardware.com/ for example.)
On the laptop vs. desktop issue, just consider that upgrades and repairs to laptops in many cases are much higher than the same for a desktop. And be aware that you mostly likely will damage a laptop, no matter how neat you may think you are. I once tripped with a glass of water in my hand. A single splash landed on my laptop, and it destroyed the keyboard and CD drive. The repair bill was so excessive I simply bought another system.