What, exactly, are you asking? AR10 vs AR15 vs LR308 "platform"? Or simply what caliber upper? Or brand? Just to shoot? For SHTF?
I don't think there's a one-gun-does-it-all solution. I have an LMT slick, SCAR 17, and other fun stuff and the "just one" really depends on what is most important to you.
Just to have and to shoot then a .223 is your starting point -- light, cheap (relatively) ammo, versatile
The LMT is too heavy to hump if I were carrying my life on my back with the coming of TEOTWAWKI, but sheltering in place and keeping the marauders at bay it would be outstanding. Get barrels in .260, 6.5 Creedmoor, and .243.
The SCAR is light, relatively, but ammo is heavy. What do you think you'll be shooting? If it is targets go back to the .223. Are you talking SHTF? Many worry about shooting game, but during the Great Depression game like deer were almost wiped out in short order. In a SHTF situation with today's population you won't have to worry about shooting anything bigger than a rabbit or squirrel in short order.
Unless you're worried about bipeds. If you have no base of operations resupply would be a concern. People will buy out .223 and .308 to be sure, but those same people will have it on hand if it comes to that. If you have a base from which to resupply but you're venturing forth to search for Kevin Costner with a mail bag I think the Grendel and 6.8 SPC are very attractive. The Noveske 14.5" Afghan would be a great choice IMO if you were in a wooded area. A Grendel would be great if you lived in a wide open area.
If you're just asking about brands, everyone has their favourites, but if I could have only one I would spring for one of the higher priced options with a stellar reputation.
I have a splitting headache so I've likely not thought of everything, moreover, I certainly don't know everything. Hopefully you get enough information to make a decision that is best for you. Ideally, of course, none of us should have even bothered without first giving us more information. It's not too late to narrow it down.
If you're just trolling for action because you're bored, no worries. I don't often bother with threads and I'm probably due for my quarterly contribution. Perhaps someone who really needs information will find something useful in all the posts.