Fabric: Wool, wool, wool! Cheaper coats will have a wool blend, often with higher concentrations of polyester. Wool is warmer and wears better.
Styles:
Car Coat:
Pea Coat (could probably find these cheaper at a military surplus store):
Note: J. Crew makes a pea coat lined with Thinsulate synthetic insulation which would be super warm.
Duffle/Toggle Coat:
Trenchcoat (3/4 length shown, full length will hit the knee - tie the belt, you'll look better):
Stylish, less warm choices: (add some layers underneath)
Chore Coat:
Leather Jacket: (double rider shown)