Ride flat seems vague, I don't know which direction you want to go. Either the shocks are too bouncy or too stiff.
If they are very old, probably too bouncy and you simply need new shocks. Next comes the preference towards either a harsher ride to gain control, or a softer ride. Softer is generally better for flat, straighter roads.
There are many topics about shocks where members tell you their experiences, but yes you may have other suspension wear contributing to suboptimal ride quality or handling, or probably both. Next comes the decision how much to replace and whether to go with same as OEM, equal ride to OEM but cheaper due to being aftermarket, or stiffer.
This includes your rear springs, they may have some sag by now. Left rear sag is very typical and can be seen by measuring the fender height above each wheel and especially comparing left to right side rear. Where to start depends on how bad that lean is, and remembering that in the rear you also have sway bar bracket bushings and links, since the rear end is more out of control than the front unless carrying a significant load.
As one point of reference, I put KYB Gas-A-Just (KG54309) monotubes on the front, and Monroe 58617
Load Adjusting Coilover shocks on the rear, to compensate for rear sag but I needed new rear shocks anyway. This combo makes for much more control but I would find it too harsh if there weren't lots of hills and curves where I drive.
If I were setting it up for more off-road or towing then I would get Rancho, Bilstein, or KYB Monomax, all of which have max dampening. For on road I would still stick with the KYB Gas-A-Just in front, they are just right for the heavier front on a 4WD or AWD 2nd gen Explorer.
