I've aired the Discoverers to 32 in the front and 37 in the back since the sticker states a 5 PSI difference between front and rear.
You've got that backwards, you want the 37 in the front tires and the 32 in the rear tires, unless you have the engine and transmission in the back of the vehicle. Vehicles that have the engine in the front are usually pretty front-heavy, so you want more pressure in the front tires to deal with that weight. Extra pressure in the rear tires of an unloaded vehicle is only going to cause a rough ride AND make the shocks work harder.
What sticker says a 5 psi difference? There's nothing
wrong with a 5 psi difference (it generally helps handling and works better for unloaded front-heavy vehicles), but I've never heard of a sticker on Explorers or with Cooper tires that says to have a 5 psi difference.
I went with the LT due to the extra ply and thicker tread so I have more protection against sharper rocks and other offroad hazards.
Unfortunately, in the 235/75R15 size, the P-metric and LT tires both just have 6 plies, but sometimes the LT tires have a little extra tread depth and so slightly thicker rubber on the sidewalls as well, making them a pound or two heavier than their P-metric counterparts. They do ride firmer because of this, though.
I was looking at the Rancho 5000 series since I'm ok with that price range and they seemed popular but I couldn't find much opinion on ride quality. Heard a lot of good things about the Monroe Sensa-Trac though.
Rancho shocks are made by Monroe. The 5000 series is fine if you just want them for the looks of an off-road brand. Just about anything is better than worn out old shocks.
Also, the rear shocks definitely look OEM. There's no apparent branding on them and they're black. Totally different from the front ones.
The stock Motorcraft shocks were all-black, but generally after this much time they will have completely rusted. They may have been replaced with newer OEM shocks, either from another Explorer or wherever the previous owner got them from.
I don't do a ton of freeway/highway driving. There's little stretches and some of them wind back and fourth but are also hilly so I'll probably never be hitting turns at 60+ MPH so body lean may not be a huge issue. I don't need shocks for dedicated offroading but I don't strictly want street/commuter shocks either. I don't expect a "cadillac" ride but something to help out with washboard, potholes and uneven ground.
Good shocks control body lean, but their main job is controlling the wheels and tires to maintain contact with the ground. The front and rear sway bars can get upgraded with polyurethane bushings if you want less corner lean without going to very firm shocks.
I know shocks and things like that are a personal choice but I come asking for help because I have no experience in choosing shocks. These will be the first ones I've ever bought and installed.
Do people use stiffer shocks for offroading?
"Off-road" shocks are generally "firmer" because they limit and slow the movement of the wheel/tire and suspension more, an action called
damping. You can either have firm shocks that control really well, or not so firm shocks that still give control, but not as much. For off-roading, you generally want more control, especially over the heavier tires used on trucks and SUVs, but slow-crawling trail rigs can also use shocks that don't damp as much because you don't need much damping when then suspension moves really slow.
Some people actually prefer soft shocks for off-roading, and many long-travel baja rigs and prerunners actually have pretty soft suspensions so they can land smoothly after getting airborne, but the tradeoff there is handling - they generally take a corner at speed like a sack of potatoes.
The big difference in shocks in terms of construction is between
twin-tube and
monotube shocks. Twin-tube shocks (like Monroe Sensatracs, Ranchos, KYB GR-2, Gabriel, OEM Motorcraft, etc.) use two oil chambers with low-pressure gas and generally ride smoother. Monotube shocks (like Bilsteins, KYB Gas-a-just, KYB Monomax, and a few others), use high pressure gas in one big oil chamber and generally ride firmer.
That single high pressure oil chamber in the monotubes also lets the metal body of the shock work as a heatsink to cool it better than the twin-tube design, but the twintube design is not as prone to failure if damaged, since one tube can still work even if the other is damaged from contact.
That's not to say that a vehicle equipped with monotube shocks will always ride rough, or twin-tube shocks will always ride smooth, but a combination of things like tire type, tire pressure, and just the construction of the vehicle and its suspension type all play a part in how it rides with whatever shocks, springs, tires, wheels, etc. are on there. The TTB and solid rear axle of the Explorer do not ride as nice as the luxury SUVs with A-arms and 4-wheel independent suspension.
My guess is with the new tires and just about any new decent brand shocks on there, you will notice a big difference and it will ride great. The "rough" ride you are feeling now is probably more to do with the complete lack of control the worn out shocks have over the suspension.
You can safely pick out Monroe (either the Sensa-Tracs or the slightly upscale Reflex) or Rancho 5000 shocks if you like those, or other brands like KYB, Eldebrock, Bilstein, etc. and you will get some good shocks that will complement the new tires nicely and make the vehicle a LOT safer and more pleasant to drive on any terrain.
You might also want to inspect other items like the radius arm bushings and ball joints, which also play a big part in the suspension performance of the TTB, as well as check the ride height and use washers or spacers if needed to restore the front end height, so the suspension beams are farther away from the bump stops, allowing more front suspension travel, proper alignment, and a smoother, safer ride.