I'm babbling today, so beware!
The skies were opened the day that I got to play a real 1958 LP Standard. It sounded like a Tele with low impedance PAF pups, but with a lower-mid presence and sag that I absolutely fell in love with! The owner said; "Hide glue, nitro finish, finished-end frets, thicker neck and light mahogany construction is the magic recipe." It sounded just as unique unplugged as it did plugged-in.
FF -> I purchased several Historic LP's trying to cop that sound, but none of them sounded like that 1958 Standard? I didn't know that Henry J. was leaving-out the most important ingredient... Hide glue! After doing some research, I discovered that 2013+ Historic LP necks were fitted using hide glue. I wanted one that was constructed entirely with hide, which led me to Gibson's True Historic line of LP's. (As of 2017, all Historic model LP's are made to the authentic 50's specs; formerly known as True Historic.) I ended-up purchasing a 2018 LP Standard R7 Wildwood Edition w/Custombucker pickups. It has the same neck dimensions as Peter Green's 1959 LP Standard. The neck took a bit to get use, but the rewards are obvious.
I want to give a shout out to the underrated LP Deluxe. IMO, the LP Deluxe (when fitted with P90 pickups) is one of the finest sounding guitars there is. Same goes with a P90 loaded Tele. A note to high-gain players... Save your money! Once you reach SLO100 level preamp gain, such benefits are lost. Any decent 70's and up LP will do fine.
Bonus clip! Here's the sound of a 50's era LP Standard through what is (IMO) one of the finest sounding amplifiers ever made.