Door jamb sticker only reflects the tires originally installed on the line. I was taught 85% of max inflation printed on the sidewall. I check and adjust at oil changes and my stuff wears evenly.
This is true since they built it, but the brand of tire could change, and the size was the only thing listed on the placard. Engineering design decided on what size/type/brand of tire would go on to the car based mostly on load rating of the tire being compatible with the weight of the car. And this likely depended on the contract with the tire company as well, but since you'd be buying the second or third set you wouldn't worry about that. But in most cases I've seen, those placards have words to the effect of "recommended pressures", etc. There's always legalese to get them off the hook. But the weight of the car, if it remains the same, won't really matter much whichever tire you put on the car. Pressures should remain about the same. 85% of max pressure is a good thumbrule, but again, adjust according to contact patch/wear.
Tire inflation care is mainly upon the owner of the vehicle. You can't depend on the service guys who change the oil or do scheduled maintenance to keep your tire pressure in check. It's like checking your oil. You need to do it fairly frequently. Make it a habit for long tire life.
Underinflation is bad because the sidewalls will flex more and the tread is planted more on the two outside edges vs. maximum contact patch across the tire treads. It's a mushier ride, but also sidewalls flexing more and get more "roll" going around a corner. Overinflation makes a thinner and central contact patch on the tire, which means it's easier to turn due to the effectively skinnier tires, but less flex in the tire, which results in a harsher ride.
If you get a decent tire gage, it's not imperative it's calibrated to within +/- 0.00001 psi of the standard, but use the same gage on all 4 tires (and spare if you check it). The tires will tell you if they're over/under inflated. If your gage says 37 and you're flat wearing evenly across the tire, you're in the sweet spot. Make it 37 psi, please. You still need to adjust to whatever the tire wear is telling you for best performance.
Best time to check them is when the tires are cool (not driven for several hours), and where the sun isn't shining on one side or the other or hasn't been. If you have Nitrogen in the tires, while it's not AS susceptible to temperature variations, to me the jury is still out on that whether it's the end all be all for inflating your tires. After all, air is already what, 78% nitrogen?
If the tires are hot after driving, you really don't know the cold pressure. But if 3 out of 4 are reading about the same and one is significantly lower, adjust it up to just under the other 3 and you should be close. The air you added will pick up heat from the air in the tire already and expand a bit more adding slightly more pressure. So getting it close to the other 3 may even them all out after a bit.