My aunt swears by broad breasted whites. She got one so big it couldn't fit in the oven dressed out. The legs were the size of venison hocks. It was HUGE!
Yeah, It was always about double the size of the wild and bourbon turkeys they had in the same pen. It only took about 15 weeks for the toms to get 22lbs while the rest grow about 1/2 that size in the same amount of time.
You are looking for the BBB or BBW; that's Broad Breasted Bronze or WHite; the white will grow a bit bigger than the bronze and is the one seen 99.9% of the grocery store birds. Hatch to market in 4 months. SUper fast growth, and a much bigger amount of breast meat. Great feed conversion. By feeding it yourself, it will taste way better than the grocery store bird.
The heritage birds are a slower growing bird and mature at usually a smaller size and with a smaller breast size. This bird can forage for some of its feed a little better than the BBW/BBB. THis bird can be bred by the back yard poultry owner. The BBW/BBB is a specially bred bird; with the extremely large breast, it needs the skills of a technician to use AI for breeding.