Buy a lower end road bike with the mounts for a rear rack. The lower end road bikes are also typically built with more dependable components. I bought a road bike for $300 dollars 14 years ago and after 15k miles it's still going strong. Anything you buy new is a waste of money.

I also believe it's good to buy something that is not quite perfect and learn how to make it work for you. The challenge of using what you have available (and hopefully free) is a good mental exercise. I learned this while serving as a Peace Corps Volunteer in Haiti. I only had one bike (my only transportation other than foot), which wasn't perfect, and had to make it work for me. Fun.