Coaster brakes were invented for wood wheels---and they remain the very best brake for wood wheels.
But a good bendix single red band hub(bendix 76 is also OK) would be the very best hub you could git for this build because there are 1000s of them ,great chrome hubs for a good look,and most important---lots of replacement brake blocks avalible!Overhaul takes about 30min if your slow.---sam PS stay away from any english coaster!