What do you envision using the gun for? Do you intend to carry? Home defense? Range only? Answers to these questions may narrow the search a bit. If you like a home defense and range gun to start out with and then, maybe later, you can make a more educated decision on a carry gun.
How much for a new Sr 22I think that a Ruger SR 22 is a good choice to start with. It is reliable, affordable, ammo (if you can find it) is cheap to practice with, fun to shoot, and has many safety features. This allows you to train more without breaking the bank, just like the many have already stated.
You can rent firearms at Beech Grove Firearms, and I've seen people there getting on-range instruction. It's a very nice, clean range to shoot at. I'd check them out.Do they have classes in Indianapolis were I could shoot different guns or is renting at range the best option
How much for a new Sr 22
Search for the many "what should I get for my first handgun" thread.
My advice in short: take a class that allows you to shoot different guns. The gun you choose at the end may surprise you.
If you want home/range, I'd definitely pick a full size handgun. Easier to shoot, easier to manipulate, less recoil, and a little more powerful.