I would actually suggest the .308 Winchester, it's a great cartridge and it doesn't recoil bad.

I would not suggest a .243, or a Savage, since a .243 isn't a manly gun, not enough recoil that gives you satisfaction, but the .308 doesn't recoil too much like a 30-06.

Savage rifles are accurate, but cheaply made, the thing about rifles is, you'll get what you pay for, and a cheap rifle tends to equal cheap quality, in comparison to mid-range priced rifles ($400-$700), the Savage action is not very easy to handle, but that all depends on what model you get, and the cheap ones have a very rough action that isn't pleasant at the shooting range.

It all depends on your price range, my gun is a Remington Model 673.308. It's not a catalog item, or on the website, but it's not custom.
I have noticed that certain gun stores have them for sale at cheaper prices than normal, why this is I don't know, but at 100 yards, using Federal Powershoks, I can have a3/4 inch group easy, with a proper rest.
It'svery accurate, and it's a beautiful gun, the stores sell them for approximately $585.
It might be steep for you, though, because you'll have to buy a scope, too, and the best, cheap scopeI have seen is a Shooter's edge 3x9x40, or3x9x50. For $100. It's really cheap, you can look online for a retailer called Nation's Best Sports, and theydo sell them, if you don't have anyShooter's Edge products at your local gun dealer.
So, the gun, at lowest price would be
$585 (Not counting tax)
Scope
$117
4boxes of Federal Powershok
$44(Not Counting Tax)

This is all thebare minimum, you will also need a cleaning kit, those usually cost $15-$20.
If you want a sling, that's another $10-$15-$20.

It'll take lots of allowance money, if you're a teenager, to get that gun, I got mine because I also had friends and family pitch in and add to my "Gun Fund" on top of what I had already saved.

One downside to the .308 is that the .308 is used in the M4, and the M14, including many sniper rifles in the U.S. Military, and with the war going on in Iraq,coupled with high metal prices, .308 ammo isn't as easy to find as it used to be.
Shooter's who own .223's also have this problem, since the .223 is used inthe M16, and I think theSAW, but I'm not sure.

But, the .308 is a great cartridge. That's my vote.

The 7mm-08 would also be a good choice,but for now the factory ammo availability isn't so great, as far as different loads are concerned, the .308 is better in the fact ithas more ammo availability.

If you need to go ultra cheap, get a12-guage shotgun, and use slugs if you can get a rifled barrel, if you can't get a rifled barrel, use rifled slugs in arifled barrel.
You can get a great Mossberg 500 or Remington 870 for $200 or less.

I wish you luck.

BTW, (By The Way)I do notlike the .243, I just chose the name Younggun243 before I actually owned a gun.