There are a huge number of possible answers. Taste preferences differ, and there is no perfect fig. There will be some problems with rust, splitting, souring, bugs, etc... With that said, here are a few that seem to be loved by almost everyone who grows them.
Lightish- Dalmatie/Stella, Strawberry Verte
Brownish- Longue D'Aout, Improved Celeste
Blackish- Figo Preto, LSU Scott's Black
Search the forum for their names, you will probably like what you read.