I agree with just starting out with some sneakers to see if you like it. IF you enjoy spinning, I wouldn't go crazy and purchase a pair of top-of-the-line spin shoes [save those for the outdoor stuff ]

For spin class, I actually just use the very first pair of cycling shoes that I ever purchased: an old pair of Pear Izumi Vagabonds. I put SPD clips on and they work great. They aren't the most attractive shoes, or breathable shoes and they certainly don't have a carbon platform, but for indoor class, they are just fine. You can probably find a myriad of broken in (i.e- comfy), used cycling shoes on Ebay.