4x or 5x tippets should work best for the size flies most fished.
I would stay away from 6X or lighter except when fishing tiny flies (which should be avoided by a beginner anyway).
Using too light of a tippet causes breakoffs like you mentioned, and may cause your tippet to twist.
There's no need to have to deal with really light tippets, especially for a beginner.
Here is a chart which matches recommended tippet size with fly size along with some valuable info about tippets written below.
Good luck.