Tbh mate, I find hairstyles that suit me through trial and error! Long, short, straight, curly, undercuts, fringe, quiff, slickback, I've done them all. Most of them I look back on in horror but the short, textured, messy quiff is the most happy I've been with my hair so far.
As for you, what about looking at Eddie Redmayne's styles? He is one dapper ginger.
Here's a sort of longer foppish messy look, thrown back off the face: Google Image Result for http://freeimagesarchive.com/data/media/248/eddie%2Bredmayne%2Bborn%2B1982.jpg
A more tamed version: Google Image Result for http://25.media.tumblr.com/tumblr_l2zwrwqCJE1qc2gv9o1_400.png
I think the key to your problem is embracing your hairs thickness and mess. Don't try and flatten it, tame it and suppress it, that's the WORST route to go down.
Throw a bit of mousse into your hair while semi dry. Mess it up then use a brush and your fingers to blow dry it into the shape you want, being careful to keep some natural movement in there.
Then use a dry matte product to finish it off. The cut is the MOST important thing. Eddie has it shorter on the sides and the back (still only scissor cut though) and longer on top, with plenty of texture.