There's no such things as "best." There are lots of good ones, and which is "best" for you depends on what you're looking for, and maybe how many bugs you're willing to put up with. TW-based ROMs tend to be more stable and reliable on the GS3 than AOSP-based ROMs or CM ROMs. MOAR and Wicked Sensations are TW ROMs that are much faster and smoother than the stock ROM, so you might want to look at those.
But you can fix most of the lag from TW just by using a 3rd party launcher, like Nova, and changing a couple of settings in Developer Options, without rooting at all.