For someone who doesn't reload or own other rifles, the .243 is tough to beat. The ammo is cheaper and easier to find. The round itself is adequate for deer, and devasting on varmints of any size at any reasonable range. Light recoil, generally very accurate. I just picked up a Stevens 200 and several boaxes of Federal Power Shok ammo at Sportsman's Warehouse, $259 for the rifle, and $9.50 per box for the ammo. Mounted a Nikon Buckmasters 4-14X SF scope on it and after a brief sight in session at the bench (3 shot groups at 100 yards around an inch and a quarter with factory 100 gr loads about the same with 75 gr HP (both Sierra and Hornady) handloads with 38.5 gr of IMR-4064. Went out on Memorial Day morning and nailed my first coyote at about 275 yards with one of the 75 gr Sierra HP handloads. Then watched my buddy explode a rockchuck at the same range with a 80 gr Sierra Blitz BT. I finished up flipping my own chuck with a Nosler 80 gr Ballistic Tip. Fun morning!
I have owned a 7mm-08, and while it is an excellent caliber for medium game, it definitely has more kick than a .243. And while I haven't shot a .260 Rem, I have a HOwa 1500 in 6.5x55 which is a very similar cartridge that also is very light recoiling, kicks noticeably less than my old 7mm-08 Model 70 Ltwt Carbine in 7mm-08. Of course the Howa is probably a full pound heavier than the carbine was. I do really like the 6.5x55 caliber and believe it is a better deer cartridge than the .243, but only if you are a handloader. The factory ammo, while sufficient for deer, is loaded pretty mild. I chronographed the Federal 140 gr power shoks at just 2300 fps 10 feet from the muzzle. So, if you don't handload, go for the .243. If you do handload, but don't like recoil and don't plan on shooting varmints, go for the .260 Rem. If you want to hunt big deer or larger game with reasonable recoil, the 7mm-08 is a great option, even if you don't handload. There seems to be more and more 7mm-08 ammo being offered all the time.