.308 is the 'usual' battle rifle caliber. SCAR, FAL, M1A, HK 91/G3/PTR 91, Tavor 7, and of course the various flavors of AR-10. You should be aware the AR-10 rifles use a variety of designs and will generally not interchange parts outside the brand, like we are used to with the AR-15. I would suggest getting one that uses the SR-25 magazine pattern.
The SCAR is probably the lightest of all of them, a bit on the expensive side. It has a reputation for beating older and cheaper optics up.
The M1A is a bit obsolescent compared to modern battle rifles. Scope mounting is a bit awkward and the accuracy will generally not be up to the modern competitors, but it's a fun historical rifle to own.
Much the same can be said about the FAL. Those tend to be battlefield accurate and nobody is shooting matches with them. Scope mounting is an afterthought as well but it can be done. One thing about the FAL is that its 10 position gas adjustment means that you can get it shooting very soft. That and its storied reputation as the right arm of the free world means it's one of my favorite battle rifles to shoot.
The HK91/G3 pattern is similar. Recoil on these is notoriously harsh compared to some of the others, and unless you get a modern clone like the PTRs with the built in optic rail, optic mounting is a kludge. Accuracy is OK but not outstanding, about on a par with the M1A and FAL.
The Tavor 7 is a bullpup and has a lot of modern features. Great triggers are possible, optic mounting easy, uses SR-25 magazines, 4 position gas adjustment, and accuracy is fairly good. But bullpups aren't for everyone.