What kind of shooting will you be doing? A .22 is the cheapest and great fun and all you'll need if you're shooting less than 100 yards and only shooting targets and small game. A .223 centerfire will allow you to shoot out to around 500 yds and can also take some larger game at closer range with well placed shots. A .308 will take any game in north America as well as shooting out to 800 yds on the range (yes, I know all of these calibers will shoot much farther than what I just said, but keep in mind these are ranges a beginner can reasonably expect to shoot out to).
So do you plan to hunt with this gun or only target shoot? Do you have access to a 500 yard or a 1000 yard range?
There are lots of other calibers, but these are cheap, easily obtainable calibers that time has shown can be extremely accurate.
No matter what caliber or type of gun you get, you'll probably want more later on.
One final piece of advice, buy a decent scope and good rings/mounts for your scope. If you skimp on the scope, you'll only get frustrated and spend more money later on to upgrade.
Good luck with whatever you choose!