Root it you'll love it. Root does not speed up the phone. Rooting will allow you to take backups (Titanium back up, etc), screenshots, and other things.
Once you root, I'd advise looking at putting new ROMs / kernals that are faster on the phone.
Once you root, do not update to new updates. Look for XDA Roms that have the new updates instead. If you update Over The Air, you will lose root.