I acquired a .308 rifle as my second rifle ever and have owned at least one ever since. I am primarily a hunter, not a target or military style shooter. I like the cartridge a lot. To me it's a "Goldilocks" cartridge, not too much, not too little, just right for most of the shooting that I do.
I have gone though a lot of .308's over the past 50 years, always upgrading / trading when I thought I found a better one.
I think Sako got it right with their older models, with an action sized correctly for the cartridge and great build quality. But there are other good choices. A list follows of the .308 rifles I've owned, favourites are marked with an asterisk *
Savage Model 110C
Remington M700 BDL
Browning Safari FN98 Pencil barrel lightweight *
Savage 99F *
Parker Hale M98 Safari
CZ Brno ZKK 601*
Sako L579 Standard *
Sauer 202 Stutzen *
Sako M85 HB Fluted Stainless
Sako L579 Deluxe *
Sako AII Deluxe *
I still own and like the three in bold