I doubt they would care about the sole, and if the logos are small they won't care.
I would suggest getting a stethoscope, etc. beforehand. They're going to tell you to get a cheap stethoscope beforehand (something you wouldn't mind losing). Don't go out and buy a Littman Cardiology III or some ****. I personally bought the Littmann Lightweight. Not terribly expensive, but good quality. Honestly, the biggest thing about it was the good seal of the earpieces.
I went to the Florida Department of Health for everything. You're not going to find a cheaper place, esp. since I didn't have health insurance. Go on a day when you have nothing to do, because you're going to be waiting a while.