I don't know much about the Accord's suspension, but seeing as the Acura Integra is an offshoot of the Civic (albeit highly modified for performance and handling), I can probably make a good guess there.
1990-93 Acura Integra is referred to as the Gen2 series by Honda enthusiasts. You can get aftermarket rear shocks for it, but not fronts, so there isn't a lot of tuning you can do. I would guess that the `92 Civic fits into this category as well. Because the Civic is lighter than the Accord, it will get a bit more performance off the line. It may have a little bit different gearing ratios, but the best place you can find that kind of info is here:
The Gen3 Integras ran from 1994-2001. If the Civics are like them (and they should be fairly similar), these have a much more modifiable suspension, as they are 4-wheel independent double-wishbone setups. I have aftermarket coil springs and 4-way gas adjustable shocks on my `Teg, as well as an Integra Type-R rear swaybar, which increases the stiffness of the car by quite a bit and improves handling.
If you can't do the work yourself, you probably don't want to do mods, they suck up money, and in many cases, gas mileage (i.e., I have 17" wheels on my `Teg, and it has a definite impact on fuel economy). Often older parts that work fine (i.e., shocks) can be corroded to their mounts, making removal a complex process that requires a torch. Mods can also increase the maintenance cycle on the car itself, and you certainly don't want to do engine mods on a 10+ year-old car without doing a complete engine rebuild first, or you could drastically shorten the car's engine life. My car has no engine mods, and 156,000 miles on it. Kept in good shape, I should see 200,000 without a problem.
Finally, for the sake of all that is good and holy, don't add a coffee-can mufler, 2-foot rear spoiler, ground effects, lime green paint, or any kinds of flames. Contrary to what you may have been told, they do not add horsepower.