I've been rooted on my Note 3 since day one pretty much... No performance impact. As others said root alone won't cause performance issues... If you root and tinker with things.. It could.
I'm just gonna go out on a limb here and say something, it's not meant to be rude, but please don't root unless you completely know what you're doing. If you have an older phone that's not your daily driver, practice on that. Your carrier usually will not help you unroot.