I completely disassemble and fully clean and fully oil & grease mine after some shooting......preferably immediately after (and if that's not possible within a day or four)
I prefer immediately after firing...especially if I'm going to put the rifle up for a few weeks months, or longer, as I don't get to fire it a whole lot.
Leaving a dirty rifle in storage for months at a time is not a great idea in my opinion. I like to know that when I have to grab it if/when SHTF, that it IS READY TO GO.
All my rifles and handguns are put up & clean as a whistle as I type this.
A set of bore brushes, jags, and cleaning patches , and/or a bore snake , along with a good bore cleaning fluid will all accomplish getting the bore clean. Spray cleaners work well on the parts and receiver. And a quality gun oil and some gun grease for lubing & metal protection and moving parts is a must.
I always try a magazine full of "dummy rounds" to be sure it is in perfect working condition, after cleaning & reassembly, to be sure it's RIGHT.
As for not damaging screw heads....a simple gunsmith screw driver and gunsmith screwdriver tips are pretty inexpensive.
I use a "Winchester Screwdriver Gun Smith Kit" I bought online for @ 12 bucks and then purchased two sets of the Brownells rifle model specific tips for those stubborn ones and to have spares. (Brownells sells rifle model specific screwdriver and gun screwdriver tip kits for very reasonable prices)...and the specific tips are made to perfectly fit the screw slot/s....so there's really no good excuse for messed up screwheads.
A decent gun vise is also a great thing to have and use.
To each his own............