There are some around here who have their way of doing things, and if you choose to do it any other way you are Forever Damned. Take their condemnation with a big grain of salt.
Depending on how stable temps are in your dorm, temperature control is likely going to be a concern. First thing to get is a good probe thermometer (a probe on the end of a long wire, connected to the display on the other end). Radio Shack has a few models if your pet store doesn't carry them. That'll let you see what the temps actually are in the snake's enclosure. Get the probe down at the snake's level - it doesn't really matter what the temps are mid-air. To add heat, you're looking for an undertank heater, or UTH. There are some itty-bitty ones that'll stick under one end of the shoebox you have, rated at 4 or 5 watts. That'll be plenty big enough for an enclosure that small. Another thing you'll definitely want is a way to adjust the output of the UTH. The cheapest way to do that is with a dimmer cord, a lamp cord with a dimmer built into it. If you go to Lowe's or Home Depot, go to the electrical department, and ask one of the people there, they'll be able to point you to one. They run $11 or so, and are rated up to 300 watts, so you'll be able to use the same dimmer as you increase enclosure sizes. To tune the temp, check it right down on top of where the UTH is, under the substrate, and adjust it with the dimmer. With the combination of a thermometer, UTH, and dimmer cord, you'll be able to tweak the temps just fine.
As for substrates, the paper towel route is a nice cheap and effective way to go. The snake isn't going to care. The hides you've provided will give him the security he needs. When the paper towels get soiled you just replace them. When you're at the pet store, you might take a look at the aspen. It's not very expensive, and it treats snake poop sorta like kitty litter would. You can just remove the small amount of aspen around the poop or sloshed water and toss it. The terry towel seems a really good idea to me, too, but you'll have to keep scrupulously on top of cleanliness, and probably have several in rotation. That could get to be a real hassle really quickly, I'd bet.
I can identify with having ...um... "contraband critters" in a dorm. Unless there's a full G.I. inspection, you should be able to keep things under control. One other consideration - is the cupboard mostly open or mostly closed? If it's always dark, that's not the best situation. Corn snakes do their thing around sunrise and sunset, and hunt by smell and sight, so they do need to be able to see.
Get to know the herpers in the Herp Society at school. I was pretty heavily involved in it at A&M back before the earth cooled, and several of them were very knowledgeable and helpful.
Let us see pictures as your snake grows! Good luck!