Versatile breeds can handle most hunting tasks. They have the genetic make up to track, hunt air borne scent, and are very trainable. Wirehaired Dachshunds are used for tracking and while they move a little slow are good at blood tracking. They might also move rabbits out of a brush pile for you and this would be a fun way to hunt.
Another choice would be one of the working dogs. Belgiun sheep dogs, Lab's and German Shepherds both do well at tracking and may well produce small game for you. Border collies are another idea
So, in the end I'd suggest either a Drahthaar, or a Kurtzhaar from German lines as my first suggestion. But looking into any of the others as well is a good idea. Try to see them working before you make up your mind.