As a dude that lifts with a permanently separated shoulder that also had shoulder problems for years, I can tell you a few things that I have done, or do, to keep them at bay and/or some of the changes I have made in training certain movements.
For bench - Close grip only. Yes, you can bench more with a wider grip, but you can also get a look at a t-bone by sticking your head up a butchers ass......wait, wait. Anyway, If you plan on lifting for a long time and want to save your shoulders, bring your grip in. My grip is 15" between the index fingers. This usually puts me right on the outside of the inner smooth of the bar. You don't have to go this close, but bringing your grip in will take a lot of strain off the shoulders and rotator cuffs.
For incline - As John Meadows just posted recently, when you do inclines and lower all the way down, it places much more strain on the cuff. Many years ago, I read about Flex Wheeler and Chris Cormier doing inclines where they lower to right below the chin. Seeing how inclines always made my shoulders feel like shit, I tried this out and to my surprise, I had no pain with it. I've stuck with it ever since. Of course, keyboard warriors will tell you "you didn't touch your chest" but I've never seen an incline press done at a powerlifting meet. And I also don't think that inch difference is going to make that big of a difference in how much you can press. If anything, I always found it harder, but easier on the shoulders. So a win/win. Also, incline tends to give good carryover to both your overhead work, AND the bench. My grip on incline is not narrow, but it's definitely not wide either.
Press behind the neck - The behind the neck press has gotten a bad rap for YEARS. Why? Because of people who lack the shoulder flexibility to do it. Think about that for a minute. Does that make the movement dangerous, or just dangerous if you try to overload on it, while you aren't flexible enough to do it?
Most people, when they start lifting, aren't flexible enough to squat properly either. However, we're not in the business of telling people not to squat deep because they lack the flexibility to do it are we? No, because we're not certified personal trainers. We're lifters. If we suck at something, we work to get better at it, rather than feeding a handicap.
I remember years ago when I was doing DC style training, Dante had guys with shitty shoulders doing shoulder "dislocates" with a broom or band. They RAVED about how great their shoulders felt after getting good enough to do them. I was able to do them right out of the gate, and it never made my shoulders feel better. You know why? Because I was still doing press behind the neck. Shoulder dislocates don't look a whole lot different than press behind the necks really. And all the guys from the 70's and 80's loved them some PBN and I don't remember any of them having their shoulders explode out of socket like something out of a Die Hard scene. The difference with the press behind the neck as opposed to benching, is that you need to get your grip WIDE. Not close.
You don't have to go snatch grip wide, however the wrists will need to be well outside of the elbows, not in line with them.
It goes without saying that you need to do cuff work. You should throw in some easy cuff work before any pressing, and after as well if your shit is really bad.
Let me also add, that I think pressing twice a week is enough. Most guys can eventually gain strength just fine on once a week. The whole premise that you need to press 3+ times a week seems like a sure fire route to shoulder problems, and the majority of really strong pressers I know, don't train the press more than twice a week AT MOST. And plenty of them train it once a week.
I hope this helps some guys out, and may you use it in your pressing programming to get better.