Buy a 1990s rigid (no suspension) mountain bike on Craigslist for $100. Make sure it is a good brand, not a Huffy or other Walmart type bike.

It will be rugged, cheap, and have low gears for your hilly ride. Rigid mountain bikes are excellent commuters.

Get a helmet $30 and lights $40-ish. Also get a quality U lock $50 and learn how to best use it.

Later you can add street tires, fenders, etc.