I'm also a rising junior in college and I landed an internship last year. It was my first "office job" and I didn't have that many business clothes. My recommendation is to spend a little bit of money on just basic shirts and pants, maybe a suit if neccessary but don't buy stuff because you need stuff. Just buy enough so that you are not wearing the same thing everyday, and slowly shop of work clothes. I dislike shopping for work clothes, but I need to keep in mind to look for shirts or pants for work as well as t-shirts and jeans.
As for stores, Banana and JCrew are pretty conservative. If you want something younger you can try Express, but it depends on how conservative your firm is. I find that NY& Co.'s fits are for older women. Although they may be inexpensive, you may not like the fitting of their clothes.