Caroline,
Buy the bike.
You already have the desire to ride and that's half the battle. My first bike on returning to cycling in 2000 was a nice Huffy, 50lbs of shoddy welds, inferior components, crappy chinese tires and cheesy grip shifters. After riding it for the first time and passing out in a neighbors yard, I put 600 miles on it, donated it to my inlaws and moved up to a $600 middle of the road Diamondback and later to a Trek 2300.
The Huffy came to me in a box and I assembled it myself, I don't trust some of the hamfisted greenhorns at W-mart and for that matter at my LBS. Used is always on option but you have to be fairly in the know to make sure that you're getting a good deal. There are any number of people on this board that can give advice if you forward all the details.
If you keep your interest in riding, the cheap bikes make the better, lighter bikes seem like rockets. Since your commute is only a mile, there should not be any breakdown that will leave you terribly stranded.