I recommend getting a Silkie.
I have had really good luck finding proven Silkie brooders. Silkies are very broody prone, and Silkie breeders will often use one that is less than perfect for looks but an excellent mother to hatch their breeding stock. They retire them out around 2 to 4 years of age. I purchased one at 2 years for about $20 then was given one at 4 1/2 years of age. They can live up to 7 or 8, and will brood contentedly about every 3 to 4 months pretty much through their lifetime.
They are smaller, so you will have smaller clutches, about 5 to at most 6 large fowl eggs, or twice that for banty size, depending upon the Silkie's size and "spread factor."
Bantam Cochins can be a good choice as well, and are common birds for 4H-ers. I purchased a bantam Cochin from a turkey breeder who was using a flock (and I do mean flock) of banty Cochins to hatch turkey eggs. I purchased 2 pullets from her that were out of a very broody mother, and I've already been rewarded with a good brood from the older one at 8 months of age.
LofMc