I always do a brief on-stage warm up for gigs by with about five minutes' worth of material:
(1) Two minutes : Play through some jazz chord progression like "rhythm changes" to loosen up my left hand, and to get my hands calibrated to the scale length of the instrument. I do this because I play four instruments with different tunings and scale lengths (guitar, baritone guitar, Warr guitar, banjo), and I like to awaken that muscle memory.
(2) Two minutes : Play through some three-octave scale, up and down the neck. I happen to be in a Dorian state of mind lately, so that's been the scale of choice. I don't try to do this at any degree of speed. The point of the scale is to make sure the notes speak cleanly across / up and down the neck. Most of the time I do the scale warmup at around 80 BPM. It's pretty slow, as I want to pay attention to my pick attack, economy of motion, and the condition of my strings / frets.
(3) One minute (unless the rest of the band joins us) : Noodle on some random song passage for fun. If I'm doing this onstage as part of our line check, I'll often kick into a song for the amusement of my bandmates (who often will jump in and join me). We did a fairly rousing version of "Spirit of the Radio" at a recent sound check. I'm a big Rush nerd, so it's easy for those songs to volunteer themselves from my subconscious.
We usually do (all or most of) two or three of our songs as a full-band soundcheck.
Once we're done soundchecking, I do a final spot-tune on my primary guitar. Then I take my backup guitar and retreat to the green room, and spend at least 30 minutes of focused practicing and really warming up. I like to use a metronome for 10-15 minutes to lock into a steady rhythm, then free-roll while I play through material for the show. I like to have my backup guitar with me until we head to the stage. When it's time to play I just carry it to the stage with me and leave it on the stand behind my primary guitar. I don't take my primary guitar to the dressing room because I want it to stay onstage, and remain at the same temperature as the space where I'll be playing it.