Places to buy, you're going to be slightly limited. You can shop online somewhat, but anything you buy from out ot state will have to be transfered to an FFL dealer in your state first. This usually costs around $20-50 (I've heard even higher in California). Check out local gun shops and see what they're like - you can always price compare online to see if you're getting ripped off or not. Some gun shops are way overpriced, others are reasonable.
The most important thing you should do is check out local ranges that rent handguns and see if they have any sort of "first time shooter" programs. Rent a few guns and try them out to see what you like. I wouldn't buy anything without shooting it first.
As far as caliber, I'm a .45ACP fan myself, but it's not always an ideal caliber for a first time shooter. It's expensive to shoot (~$250-350 per 1000 rounds), so you might be detered from shooting by the cost of ammo. The recoil isn't bad, despite what a lot of people say. Last week in our Monday night league, we had a scenario where we had to put 2 shots on three targets, reload, then put two more shots on three targets. The guy who shot it the fastest did it in 12.22 seconds - with four seconds of penalties, which means he did 12 shots, including a reload and the draw time from his holster, in 8.22 seconds. He was shooting .45ACP, so even with the recoil he was able to pull off fast second shots.
9mm is quite a bit cheaper to shoot at around $160-200 for 1000 rounds. Of course, .45ACP gets cheaper to shoot if you reload, but you've got to buy all that equipment first. I wouldn't reccomend reloading right away, once you start shooting 10,000 rounds a year or more like my Dad and I, then it's time to look into a Dillon progressive press.
For a first gun, check out the Springfield Armory XD line. They have a variety of pistols and they're universally well-liked (except by Glock owners

). You really should try whatever you're thinking about buying before you shoot it though.