Play bikes and work bikes are so different that it is worth having 2 bikes, if you have the storage room.
For an everyday campus commuter, you shouldn't spend too much because of security issues. You need enough quality to be durable and reliable. $300-800 midrange bikes are usually a good bet. You also need to budget for accessories such as lights, fenders, luggage racks, panniers, helmet, lock, repair kit and you need to run some premium, puncture-resistant commuter tyres to get you to school on time
In hilly terrain you need a triple front chainring, so 24 (3x8) to 27 (3x9) gears (the number of rear cogs makes minor difference).
You need tyre clearance for medium sized tyres + fenders. In snowy areas you need extra clearance for studded winter tyres.
The wheel size, 26" MTB or 700c hybrid makes little difference for commuters. I have used both.
Brand makes little difference in the same price bracket. You may want advice and backup from a local bikeshop so pick your shop first. Get a bike the right size.
Used bikes can be good value if they are not worn out.