I'm tusseling with the same question myself with regard to the 7600 pump. I already have (2) 760 rifles, one is an '06 and the other is a .300 Sav. Not that I need it, but I'd like to get a pump in .308. As you can see I am partial to the 30 caliber. I will probably go for the 7600 rifle and have the barrel cut to 20".
Like the 7600 carbine , the 7400 carbine only comes in the '06 unfortunately. So if you really want the 7400 carbine, the caliber question is answered for you. The new Rem. model 750 carbine comes in .308, .30-06, and .35 Whelen. More choices, also more $$$, as usual.
If you're hunting is limited to deer / black bear sized game, the .308 is all you'll ever need. You can even use it for moose and elk, up to 200 yds, WITH WELL PLACED SHOTS! I mention this because it has been done...a lot! It may not be the first choice for many, but I wish I had a dollar for every elk and moose that was taken with a .308.
I don't know how many rifles you have, but if you're just starting to build your collection you can't go wrong with the .30-06, followed very closely by the .308. Ammo is priced about the same for both. As far as barrel length goes, I'd say it depends on personal preference. A carbine can do everything a rifle can do, just in slightly lighter and more compact package. For plinking get a .22 rimfire.
This question of best barrel length and best caliber, especailly .30-06 vs .308, is never ending. I, like many others, have answered it by having a .30-06 rifle and carbine, and a .308 rifle and carbine. Crazy?...Absolutely!
One thing to think about is state regs on semi-autos. They can't be used in states like Pa., maybe others I'm not sure. This may not be an issue for you, just wanted to mention it.
Good luck.
NYHunter