Jack,
Last Spring I built the same machine from Patrick's site.
You're going to have lots of fun (and maybe a little frustration at times) but will end up with a very useful tool and will learn an amazing amount along the way.
I don't envy you cutting everything by hand. Do you know anyone with a tablesaw? At the very least have the lumberyard or hardware store cut the MDF into strips with a width that fits tightly into your mitre box.
Since you're an EE student you should check with your department chair to see if you can turn this into a special projects class for credit. That might also help you get access to whatever shop facilities they have.
My advice on the motors / drivers is to buy the best you can. You can always resell them for a reasonable fraction of your investment but likely you'll want to build a 2nd machine using your first to cut parts so you can have greater precision and rigidity. It's nice to be able to reuse your motors. I bought the Keling 425 oz/in motor package for my first build and am reusing them on my current, larger machine. The G540 package from Keling (I think it's $579) is better still but wasn't available when I built my machine. I have friends who used the hobbyCNC pro boards very successfully as well.
Let me know if I can help answer any questions that come up.
Gordon