I just bought honda fork oil for my SV650s. The stock suspension is really weak. From what I hear, 20W was too stiff, and the store didn't have any 15W, so I got the 10W. I have yet to actually do it, I will keep you posted.
Go to Racetech's site and plug in your info, they'll give you a good weight to start with. The SV works best with 20 to 30 wt. oil in its antique damper rod fork (10 is stock). The TLR is going to take more like 5 wt.