Congrats on graduating.
Moving a leased vehicle from one state to another is generally not a problem. When you move you call the bank and tell them to send you a power of attorney document so that you can re-register the vehicle.
The things you have to consider when doing this are (1) most states will not refund you the balance of any registration charges / upfront taxes when leaving the state, so you should time everything so that you move right before the registration anniversary and (2) you may end up having to pay more tax in your monthly payment depending on the taxing jurisdictions you are going to and from. Someone more knowledgeable here can probably speak to the specifics of MN and UT.
Get AWD sure, but good tires are far more important than AWD/4WD. If you know you are going to have to be on the road in crappy weather, invest in a set of snow tires and have them swapped every winter.
Many banks will write a 7500 mile lease; some will even write a 5000-mile lease but those are rarer and are mostly seen on $$$ vehicles.
Check the broker deals in the Marketplace section here. Even if there aren’t any in your state or area you can use these as templates for putting your own deal together. Also look into brands that offer new grad discounts such as BMW. Most brands offer first-responder discounts which you may also qualify for depending on the brand.
This post has some good next steps (it’s from 2021 so ignore the part about it being the worst time to lease lol): New to lease a car. What is next step? - #3 by mllcb42