The blade is only one part of the equation. The tablesaw and how it is set up are the other two parts.
Forrest blades are manufactured to exacting standards. They are the only blade I will use in my shop (unless I am cutting junk wood then I use a cheapie that im not concerned about ruining)
I have a cabinet saw, a delta contractor saw and a bosch portable saw. The same Forrest blade will leave a different finish on the edge of a board on each saw.
Your table saw's arbor run out/vibration and how accurately the table, trunion and fence are tuned are what determines most of the quality of your cut. If you are running a less expensive or contractor saw (and I am not being demeaning here so please dont take this wrong) you are not going to realize the benefits of an expensive high quality blade like a Forrest, or the higher end Tenyru's, as they just dont have that level of engineering built into them. The best you can hope for is a reasonably straight and square cut to be cleaned up at the jointer. (and never rely on a tablesaw for your final glue joint, a nice slow shallow pass on the jointer to clean up the cut is what you need)
Another thing, if you bring your lumber in rough and dimension it yourself then use a junk blade for the rough rips and cross cuts and save your "good" blades for the "money" cuts.
With regards to a stabilizer, they are primarily used for thin kerf blades to stiffen them and keep them from flexing. Personally the only benefit I have ever seen to a thin kerf blade was for direct drive, and under powered saws that need to rely on motor rpm instead of hp to cut through the stock. They are more of a curse than they are worth, especially when you need to cut thick stock and do any type of "specialty" cutting, the stabilizer tends to get in the way or has to be removed to make said cuts.
Another big benefit to Forrest is that they are local (Made in USA) and have a service department that not only resharpens your blades to factory spec will tune the blade and repair it for reasonable fees.