I like CanGren's advice. You really can't go wrong with that list. These are good foundational garments to get you on your way.
While in grad school I found SF. SF has proven to be an invaluable resource and has saved me a lot of money and time and helped me to reduce the mistakes in wardrobe selection. Here is what I have learned and maybe it will help you too.
For approx every $20 you are planning on spending spend one hour studying the following threads. Since you are in university this part will be easy for you. Start with this thread on mistakes we have all made when updating our wardrobes. Then check out the WAYWRN: MC casual edition thread. There is a broad range of looks here but you will see all the iterations of casual wear and you can get an idea of the nuances. Follow the discussions on that thread and note the reactions (good and bad) of forum members and you will in good time understand how to put together a solid look for yourself that won't break the bank and that you won't regret buying.
Maybe make a folder and drop in fits that appeal to you and then you will start to notice their commonalities (e.g. trouser type and cut; sweater styles, shirt colors, etc). Strive for cohesion and steer away from items that are very difficult to pair with more than one garment. You will begin to find that there are really just a few variables of color you need. For example, if all you had for shirts were blue oxford shirts you could create three great outfits with one pair of dark denim jeans, one pair khaki chinos, and one pair of grey chinos. With nice shoes (in your case as a student desert boots, aka chukas, would be a good choice) and a field jacket or pea coat (depending on weather) you will look great and will not be out of context at most universities.
Start slow and be stingy with your money. I have been greatly influenced by the ethos and acumen of SF member Orgetorix who has the Thrifty Gent site. His looks kill just about every time and he barely drops a dime. Much of it is more business oriented than what you need for school but the lessons and skills are the same. And on SF you will constantly encounter the mantra that fit is everything and it is absolutely true.
Eluther makes a great suggestion. I'll add just this: Don't even take your wallet with you. See what the clothes look like on you, take a picture in the mirror, look at it that evening and then sleep on it.
Congratulations on your recent life successes and I wish you the best with your studies. Good luck with your search, you will do fine!