To the general audience (non comic fans), Hawkman is the most known of the couple. That's why it's best to begin with him.I actually like more Shyera than Carter. but I also think that could also be the other way. first Shayera and then Carter/Katar.

Say what you want about Smallville, call it garbage, but there's a reason why Hawkman was on the show and not Hawkgirl.