Stabilizers do a few things when screwed into a bows' riser. They help balance a bow when in your hand, helping for a steadier aim. And they also help to dissapate any left over energy not transmitted to your arrow upon launch.
What you need to do is find a pro shop that will let you shoot your setup with different stabilizers. Obviously choosing the stabilizer that feels best to you. As for a magical number with the weight or length of the stabilizer, that can only be found by trying different ones out. Personally, I prefer 10 inch, heavy stabilizers when 3D or target shooting, and light weight shorty's when hunting.(around 6 inches or less.)
Please remember that in some tournaments, there are rules you need to follow in terms of stabilizer length, type of sight and so on.
Tweak, tweak, tweak...