I keep them clean. I use blitz cloth or dunlop 65 on the strings - I'll run the blitz over & underneath the strings up and down the neck, then repeat with the dry cloth. I wipe down the guitar quick and use some polish, my right forearm sweats a lot all over that lower bout and leaves a big cloudy area, I clean and polish weekly, but I usually have 3 out at a time. If not playing for a few days, which suck, I put them in the case. The acoustic goes in the case when not playing and the case has the humidor with bluetooth (D'Addario). I only use oil on the fretboards probably 3-4 times a year, unless needed otherwise, and applied sparingly. I will clean, polish and wax my electrics every few months with gloss finishes. . I have all kinds of cleaning stuff, a real light sandpaper for frets. Check the intonation all the time, and neck relief. It changes here in Illinois. Midwest humidity, and usually at least a couple months of real cold weather, possibly brutal winters. Change strings as needed, usually every week when I'm playing everyday, which is what I like to do if my job allows it.
The Music Nomad stuff is really good. It was developed by a guy who's worked for decades as a guitar tech. I got a real complete set of feelers for more exact and the less relief the Suhr & Friedman do well with.
I wash my hands a lot anyway, but always before playing, and alcohol sanitizer, and put my left hand finger tips and right thumb and index in isopropyl alcohol - dry is good for the calluses. Screw skin care I'm not a hand model.
The larger screwdrivers from a good eyeglass kit, Nut Juice, Big Bends, tons of microfiber and flannel cloths, soft towels. I have experimented a lot with strings but I think I'm going back to D'Addario for electric and acoustic.