lol it's kind of ridiculous how the term "normal" gets thrown around so much as if it were something to be desired. Besides, ask 100 people what normal means, you'll get 100 different answers. For me, "normal" people are kind of boring and superficial. "Weirdos" in my book can be nonconformists and are usually pretty cool because they dgaf what you think.
You shouldn't be deciding to do an away rotation based on what your personality is. If you want to do aways, go for it. I personally think 1-2 aways would be good for most people who want to do any in the first place.
FWIW, I know a couple "normal" people who did a bunch of aways and ended up not matching at any of them.