I've ridden with the following on my hybrid, Kona Dew frame:
Nitto noodle 48 cm drop bars (relaxed touring drop)
Nitto moustache bars
Nashbar moustache bars
Kona flat MTB bars
All worked just fine and had good control. I've ended up with the Nitto moustache bars after trying all.
I've also tried all the following on my racing frame:
TTT 44 cm drops (classic racing drop)
Nitto noodle 48 cm drops (relaxed touring drop)
I ended up using the 48 cm Nitto Noodles for comfort.
Determine what you like via trial & error - there's no reason not to have any type bars you like on any type frame you like. The only caveat would be for off-road riding where you may need either minimum width for clearance or maximum width for control.
The STEM on the bike seems to have more effect on fit than the bars themselves. Getting the right distance from the seat and pedals is of primary importance for efficiency and/or comfort. Not all bars will work with all stems.
Moustache bars have hand positions more forward than do road bars, and thus I find that they (moustache bars) work best for me with shorter stems. I'm also sensitive to handlebar height. I like my bars high! For this reason, stem angle is also a critical parameter for me. You'll just need to experiment to see what works for you.