United, Southwest and Frontier all consider Denver a hub. So that works in their favor. But some things to consider:
United will likely have the most flights to the most cities. But it’ll also be the most expensive.
Southwest offers fully refundable fares — a huge benefit when dealing with the vagaries and changes in a cadet’s schedule. But its flight schedule and destinations won’t be as rich as United’s
Frontier is the cheapest, if you don’t mind ordering things a la carte: Seat assignment, check. Checked bags, check. Seat belt...oh, why not...check. But it has the smallest network of the three.
My advice, having dealt with all three out of Denver: Go Southwest if it flies to your hometown.