Not sure if the 7.5+ miles is one-way or RT, but I'm assuming one-way since you didn't specify. If you drive 7.5 miles, your bike route will probably be 8+ miles. That's plenty long enough to get tired of a crappy bike fairly quickly if you bike commute to work more than one day a week. What makes a crappy bike for commuting? Fat, knobby tires, copious amounts of rust, stamped-just-for-this-bike-by-an-overseas-factory parts that can't be replaced, front shocks that add unnecessary weight, no eyelets for mounting at least a rear rack, and most importantly a bad fit. A squeaky chain might be salvageable, a seat can be replaced, old tires can be replaced, but a quality ride starts with a bike that was built to be serviced and maintained and not meant to be tossed into a landfill after a few months of riding and the first mechanical problem.
Quality used is better than crappy new and crappy new is better than crappy used. A bike that costs less than $150 in my market (NC suburbia) is either a junk bike or a quality bike that needs quite a bit of maintenance to get ready for riding. A quality used bike ready to ride immediately often starts north of $200. The three bikes my wife and I ride the most cost between $400-600--two were high quality used bikes ($400-500) ready to ride and one new bike ($600). We've put a few thousand miles on these bikes. If you're completely strapped for cash and can't swing at least $200 (especially since you don't know much about bikes), I would sell something, work a few hours of overtime, cut cable, or something similar. You could raise that little bit by the end of the next month or two.
