One good thing for you is a billion people* have attempted to achieve the balance you are looking for in Civics in the last 10 years, so Honda forums should have plenty of good info on how to get what you want.
Unfortunately, everyone's perception of what is truly neutral is different, and just because I am comfortable with a specific set up and think it handles brilliantly, doesn't mean the exact same components on your chassis will give you the same feeling. You have to remember wheel size, offset, tire size/type/temp/pressure (in addition to the other suspension components, like Chris B. alluded to) all play into handling and feel.
According to
this site your 99 had a 22mm FSB and no RSB from the factory. I also found what looks to me to be a decent write up for Civic sway bars on
JDMUniverse.com.
Eibach offers a 26mm front combined with a 17mm rear...they generally engineer their kits to provide a safe, understeer-to-neutral handling dynamic, though that can easily be tweaked into the neutral-oversteer category depending on the other suspension components being used.
Good luck.
*Might be slightly fewer than that.