Ohen choosing a new high-performance shock or strut you have to factor in a few things, such as spring rate, driving habits, ride quality, and road conditions. For general performance and daily driving, a good aftermarket shock/strut is your best bet. Whatever brand you use, make sure it's a quality name brand. You really don't want to sacrifice the rest of your suspension by using inferior shocks/struts. Expect them to last roughly 3-5 years, depending on how much you drive the car. Generally rear shocks will last longer than front struts and you may be able to get away with replacing them every other time you change the struts.
Now if you're looking for high-quality performance shocks/struts or need the adjustable kind for things like road racing, remember that your shocks, struts, and springs work in conjunction with each other for absorbing road imperfections. If you have too stiff of a strut and your springs can't handle that kind of load, then you're in for a seriously harsh ride. You should only consider high-performance shocks/struts if you're going autocrossing, drag racing, or have lowered the car over 1-1/2". Also, it is recommended by some dealers that you use a stiffer strut with stiffer springs, as the spring rate on them is much higher than stock and will eat up even decent "normal" struts in less than a year.
There used to be a number of manufacturers that produced aftermarket performance shocks and struts for the Cougar and Thunderbird, but no longer. About the only one left now is KYB. They have a GR-2 model that should give you the performance gas-filled handling you're looking for in most situations.
While we're on this subject, we should probably address the 800-lb. gorilla in the room: Mustang shocks and struts. Since there are so many more aftermarket choices for Mustang performance shocks and struts, it's very tempting to just use those instead, right? Well, yes and no. You can use them but you have to get the correct model years. Do NOT use 1987-93 (Fox) Mustang shocks and struts, no matter how tempting that may be, because they simply don't have the right travel length ("sweet spot") for rebounding and absorption that our cars require. You will have an incredibly bumpy and punishing ride as a result, with plenty of bottoming out. Instead, you can use SN-95 Mustang parts (1994-98) as their suspensions became alarmingly similar to our cars. There is still a matter of full shock travel not being perfect, but they are very, very close in spec and will bolt in with no modifications. Several readers are using them now and report no issues. If you cannot find a Cougar/Thunderbird-spec strut or shock combo that meets your needs then the SN-95 Mustang shock/strut combo should be the next place to look.
You may be tempted by the ubiquitous air shock, which uses air instead of your normal gas-charging to absorb the shock. You can fully select the pressure inside the shocks, something that you cannot do with most aftermarket shocks. However, there is again a tradeoff—a much firmer ride. And you also have to keep an eye out for air leaks. Once the air leaks out, you've got nothing inside the shocks to keep your back end up, and you can imagine what that feels like. Some people like them, some don't. The fact is, it's simply a temporary fix for keeping the back end up if you've got weight in the trunk or are towing. A cargo coil spring does a much better job than an air shock.
If you have the factory quad shocks (a.k.a. axle dampers), local and online parts stores can get replacement quad shocks and they are rather inexpensive. You may have to look them up for a 1987-93 Mustang GT as sometimes their computers don't list for a Cougar or Thunderbird; the Mustang parts are identical. Several companies do make a performance quad shock, but we really can't say what advantage they'd be, since quads are so much different than a normal shock. When pulled one way, the quads do not compress back; instead, they stay put, hence the axle dampening name. They last a very long time but should be changed every other time you change the normal rear shocks for best performance. A new set of quads works miracles in keeping the rear end under control.