If you've never shot a gun before, I'd stick to a .22 revolver or pistol, until you get the basics down. It's cheap to shoot, and you can spend a good amount of time enjoying your first time out without going broke buying ammo. I've got a Walther P22 and I love it for plinking. If you're looking to buy, I'd probably go with the Ruger Mark III or 22/45 like has been suggested. Word on the street is, they're a bit more reliable and accurate than the P22. I may pick one up someday for a bit more accurate plinking, but for now, my P22 works.
When you go to whatever range you decide to go to (I have a membership to OVO, and have no complaints) they should have a long list of general safety rules and regulations. Read these, and know them. They're mostly common sense.
After you've got down the basics and you decide to make a second trip (and you will), I'd probably step up to a 9mm of some sort (your choice). It'll get you aquainted with centerfire pistol rounds and isn't toooo expensive to shoot.