As a dude, a big thing i changed and it helped, was stop using run of the mill body soaps and such. The health store has stuff. I limit super hot showers and sometimes only soap feet/groin/pits unless its necessary. I mix hair product use, some good some bad, and dont wash it everyday.
Theres Body brushes you can get that you use before showering to help exfoliate. I also keep salt scrub and Sulphur soap in the rotation as needed.
Food Grade Oils like coconut and avocado are great for Winter dry skin. I rub on after shower is off while im standing there and my skin is wet, then i dab dry with a towel. Usually by the time im done in there, im dry and ready to dress. Its not so good if you have to shower n go, it can feel sticky when you dress.
I shave with Aveeno. Its better to me, than stuff marketed to Men. Ive also just used run of the mill Womens Shave gel too. (Ive had a beard for a couple of years, and things may have changed for Mens shave products)
When ive reduced starch and bad carbs, sugar, my skin improves. My diet hasnt been the best in a couple of years. But, i did go GF for a while and my skin improved which was an added bonus. No more dandruff shampoo!
I used to clean houses. For whatever reason, after many years, i began to notice that clients that used Cheapo OTC skin care had more dust. Since dust is supposedly a lot of dead skin, my unscientific conclusion was the body sheds more skin to get that stuff off. Idk, take from that what you will, and im aware there are many X factors in that conclusion.