Ok, I think I get it now. Badges are not all that formal, just a sign of "I'm a (insert family name here)". I really am not sure how coat of arms got brought up with this but I don't really have any interest in a coat of arms, just knowing what badge would be the most appropriate.

St Andrew's cross would not be my first choice but getting into religion vs catholicism vs christianity. I would much rather have a simple "I'm a christian".