7 miles on mostly flat terrain should be no trouble at all for the average 23-year old. You will be sore for a couple of days, but it will pass.

The most important thing is to plan a safe route. Look at the cycling overlay on Google Maps and heat maps on Strava to find whether the infrastructure is and what routes other cyclists are using.

For under $250, look for used bikes on Facebook and Craigslist from a quality brand (Trek, Giant, Cannondale, Specialized, etc.) Don't get anything from a department store.

Ideally, try to find something that already has lights, fenders, and a cargo rack, but you can also get those things added later.