You can get parts at online places like Tigerdirect.com or newegg.com.
Again, I wouldn't try the laptop deal. It's easier and less expensive to get parts for a desktop. Since you seem unfamiliar, you might want to look for a nice "barebones" kit that gives you the case, CPU, motherboard, keyboard and speakers that you have to put together, and then take it from there.
And cases are made to fit all the parts into.
If you read descriptions closely it's not hard to match things up, but you can always ask a question here, people are very friendly and helpful.
Monitors don't come with desktop cases, at least none I've seen. You could always look for an inexpensive 15" CRT or a refurbished LCD, though if you're building a desktop you might be able to just hook it up to one of the monitors around the school there.
Hope that's some help.