to the OP: 31.8 is referring to the stem to handle bar clamp size, it's pretty much the newer standard for roadbike bar(especially composite bar), it's also called oversized(compare to old standard 26.0mm)
if you need some thing that offers more than just a round profile, try those k-wing bar, the flat section is wing shaped, some people likes it, i personally don't care for it.
as far as style of bar(classic drop, compact/shallow drop, ergo, etc), you really have to try it yourself, i went from classic to ergo and end up using compact/shallow drop.
ergo for me is a poor fit because i can't get comforty enough to stay long.
if you look at your current bar, there should be label/engraving for the clamp diameter, reach and drop. get something you want based on that number/spec(baseline)