I clean my spent cases ...( in a tumbler ) ....and the only sort I do is to toss out the nasty looking ones, or ones with dents ...or some defect. ( and I sweep up range brass....so some of it may have been loaded a lot ...and some of it might have been new, and run thru a rental gun at the range...)..
I don't sort by head stamp...
I don't clean primer pockets...after the cases are resized and deprimed. I've never had a primer that didn't seat properly when I did my job right ...and no misfires ( I've been reloading for almost 50 yrs off and on / and the last 10 yrs or so, I've been shooting at least 20,000 rds a year).
I load .38 spl and .357 mag .....44 mag.....45 acp...and .40S&W and 9mm...and I use the same procedures on all of them.
Most presses don't have an adjustment to seat primers...its a question of firmly seating them...and you feel them drop in and seat. I will occasionally get a case where the primer doesn't want to go in....but its often a taperd primer pocket ( cases like S&B - are a problem )....so after I clean my spent cases, I do inspect them - and I try to catch any S&B cases and dump them in the garbage - as I sort cases into a "clean bin".