First, you need to break down what you really want. Everything you want or get comes with trade offs.
The lower you go, the ride will usually get firmer. You need to stiffen your suspension (eliminate the bounce), as you reduce your verticle travel. Once you decide on what you want, then you need to figure out how your going to get there.
What kind of money do you want to spend? Do you have a need or a desire to adjust the height of your vehicle? Do you want a car that handles as good as it looks or are you wanting "the lowered look with a comfy ride?"
So lets go with your options:
Money is not really an issue, you might consider air bags. The ride quality is good from what I understand and you have the option of "slamming" your car to the ground. At around $3000.00 + or -, it's an expensive option that has it's usefulness if you are into showing your car. A vehicle with air bags can have it's height easily adjusted, "on the fly" if you will, from switches mounted inside the vehicle. Air bags can be more easily damaged than other suspension options. It's best to talk to those that have them to understand the pros and cons of air bag systems.
Then there are Coilovers. Coilovers are a very good choice IMO because you can Adjust the height of your car, adjust the damping of the shocks (firmness) and have very good handling. Adjustments to Coilovers must take place outside the vehicle, often requiring that the weight be taken off the suspension and/or removing the wheels prior to adjustments being made.. Having these options makes Coilovers ideal for track as well as street use. At $1200.00 - $1400.00, they're also expensive.
If you want a lowered look with anywhere from stock to performance type handling, then there are Spring/Damper combinations by many different manufacturers that are available. The most common, just to give you an example would be 2 springs made by Eibach. Pro-kit springs and Sportline-kit springs. The pro springs have a 1" -1.5" drop and a moderate spring rate. Not a lot firmer than stock. The Sportline-kit springs have a 2" drop and a much firmer spring rate. Both of these spring kits would benefit from Eibach pro-dampers. The pro dampers are a performance shock made for use with lowering springs, in particular Eibach springs. (they can be used with any springs) With a moderate drop, say 1"-1.5", you might get away with your stock shocks saving you money and leaving your ride more like a stock ride. Keep in mind that with a higher spring rate, if you keep stock shocks, things may be bouncy. It all depends on your tolerance and again, what you're looking for. Anything lower than pro-springs, (like sportlines 2" drop) almost require pro dampers because the ride would be too rough and way too bouncy. Expect to pay around $230.00 + for springs and $400.00 + for dampers. There are package deals, so shop around.
***FYI - The LX platform has an independent rear suspension. There is no adjustment for camber. (front or rear) The lower you go, the more negative the camber becomes (wheels tilt in at the top) This can be corrected by installing bushings in the rear and/or new control arms in the front.
"Strut bar", "Strut brace" and "Strut tower brace" refer to the same kind of device, a bar mounted between the front strut towers. The purpose of this bar is to reduce the flex that these towers experience during hard cornering. Reducing the flex will keep the wheels in the desired position on the road, allowing the suspension to work as engineered without chassis flex changing camber and caster settings. This will help to improve traction on the turns, increasing turn-in response, and help to reduce understeer.
By solidifying and isolating the struts in their original configuration, it allows the suspension components (stock or modified) to retain their geometry and to function as designed. Typically, steering will seem quicker and more responsive, but in reality, it is the suspension doing its job properly. These devices typically cost around $300.00
Sway bars are a torsion spring that resists body roll motions. Anti-roll bars (sway bars) provide two main functions. The first function is the reduction of body lean (roll). The other function of anti-roll bars is to tune the handling balance of a car. Sway bars are one of the more noticable upgrades that can be made to a car. Expect to pay from $250.00 - $350.00 for a front and rear sway bar set.
Well that's it for starters. These are some of the basics. If you have questions, I'm sure that anyone on these forums or myself would be glad to help