As others have said, a CNC router is going to be a lot more versatile than a 3D printer. However, in a college dorm room, a router is going to be right out. It's going to be loud, heavy, and very messy.
If, for whatever reason you were still interested in a router though, you can build a very nice one on your own for your price range. If you've built FRC robots, you already have 90% of the knowledge required to design and build a CNC router.
This fella on youtube is what I always recommend people check out. He built a home CNC router out of 80/20, with great accuracy, and more than enough rigidity to cut aluminum without issue, for I think $2500 or so. He's also mentioned that he's working on a kit version that he will sell if he gets enough interest.
He's got tons of video documentation, as well as a number of videos explaining components that the average person might not be familiar with (Linear guides, ballscrews, etc)