For actual field use, sounds like the 12ga would be the best first buy. A Remington 870 (Wingmaster if you can afford it) is probably the best option for a student. If you are going to hunt deer, do yourself and the game a favor and get a rifled slug barrel or at the very least a fixed improved cylinder barrel with rifle sights. No need for a scope etc, open sights are fine at shotgun ranges. Hunting deer with a bird barrel/choke and a bead is no fun for either you or the game, and clip-on sights are crap. Trust me, been there done that in my student days. You can find combo deals on this.
A .22 is great for general plinking but also for learning to shoot well. Starting out on a 12-ga with slugs is a great way to develop a flinch and other bad habits. A Ruger 10/22 is a good fun gun, but I'd also look into a CZ452 if you can swing it. They are very nice guns and more accurate.
Check the Minnesota regs! In most states, the price of non-resident licenses will turn most students away.