Global Entry comes with an ID card similar in size to a DL. The downside is the time to get it is extended, usually a couple months from when the application is sent to when an interview (final step) can be set up with TSA. The interview is pretty easy and you get your traveler number right away and the ID card itself arrives 1-2 weeks after the interview. The cost is ~$100 and it’s good for 5-6 years IIRC.
But a Global Entry card is not an ID card as it has no photo. The local liquor store isn’t going to be impressed by a Global Entry card
A basic MN ID card will suffice for a college student.