For year-round riding and running errands, I'd look for a bike that can take wider tires (for winter conditions), fenders, mount a rack, and has long enough chainstays you can mount a reasonably size pannier without banging it with your heel every pedal stroke. Cyclocross, hybrids, and hard tail mountain bikes can handle the wider tires; discs work better in wet/wintery mess but I managed OK (not great, but OK) with rim brakes last winter.

My son's bike is an older (early-mid 2000s) Jamis Coda Sport. I think they sell the Coda line as a performance (flat bar) hybrid. Mounts rack and fenders well, takes 40mm+ width 700c tires, has long enough chainstays he had no trouble carrying loaded panniers for a multi-day C&O Canal towpath trip. Reasonably light (at least vs. a mountain bike) and fast enough I borrowed it as a fast commuter before I bought my current commute bike. You can put on skinnier road slicks for spring/summer/fall. Only downside for winter/wet is rim brakes.

You'll also want to budget for a good set of lights; watch for close outs during summer and early fall for winter gear, studded tires if you think you'll need them, lights, etc.

Another option that a friend did - he has a decent 'cross style bike as his commuter, and picked up a beater hard tail mountain bike for winter commuting. There were a couple of days last winter I'd have liked to run wider/lower pressure tires even with studs, so he may have a good idea there.

If your area has a lot of bike theft and you don't have a controlled access bike lot, or an office area or lab to secure your bike at school, consider going cheap as possible just to minimize financial risk from theft. Good luck!