Stag? LMT? DPMS? Other suggestions? And why!!! 
There are lotsa good lowers out there. What is it you want to use it for?
I’m new to all this as I only have one AR that I bought. I’m intrigued by the possibility of building an AR in 308 to use for target and hunting (whitetail, hogs, etc.). But, also considering building one for varmint hunting (20 inch barrel, etc.).
My current AR is a S&W M&P15A.
308’s are a different animal and they can’t be built on AR-15 lowers.
You need a dedicated lower and upper that work with the larger barrels, bolt carriers and mags.
There are a few options to build a 308…
Eagle Arms / Armalite (eagle lowers are available stripped, armalite only come as complete guns)
DPMS/Fulton are both available stripped.
POF is available stripped and mostly compatible with DPMS uppers once you fabricate an adapter bushing or drill out the POF lower to fit a DPMS pivot pin.
There is very little compatability between different brands of uppers and lowers.
Armalite style uppers will fit and function on a DPMS style lower, but the upper needs to be clearanced for the DPMS mags and there will be an ugly gap at the rear of the upper receiver due to the difference in profile.
DPMS style uppers will NOT fit on Armalite style lowers without significant machine work and there would still be an issue of the DPMS upper not having a stop-shelf for the Armalite style mags.
The Sun Devil billet lowers are my personal favorite.
C4
I’m personally waiting on the new Magpul lowers to come out. I think they look real nice (billet, flared mag well, abi controls, texturing on front of mag well, Magpul customer service is awesome)…thats why I want one
Grant – your favorite just for multi-caliber ARs, or your favorite in general? What do you like so much about them?
My favorite in general. I like them because they are billet without the billet cost. They also feature a tensioning screw that removes play out of uppers and lowers. Not that looks really matter, but this lower receiver has an unusual appearance to it (with the gator grip).
C4
I own a lot of different lowers. DPMS, Bushmaster, RRA, LMT, PWA and a Colt these all work just fine but nothing goes together as smoothly as a billet Sun Devil (when mated to a billet upper). 
When I first was installing a lower parts kit on a Sun Devil it felt weird because knocking in the triggerguard and bolt catch roll pins felt too easy like it was broken or something.
Ok, is their a brand to avoid?
I know a guy who has an older Olympic. He had problems getting an ACE SOCOM stock to fit properly.
Of the three you listed I would by them in this order:
LMT
Stag
DPMS
My Mega has a gator grip. Does that mean my Mega is a billet lower? I thought Megas were forged. (FWIW, my Mega is the best finished of my lowers.)