I'd try stomach first. I think it's easiest to stomach for people who are new to this. If you can get turkey stomach, just cook it long enough - e.g. in a slow cooker with bones and vegetables to make delicious broth. Hearts, in particular small ones (chicken), contain tubes, and I think it might turn you off.
If you think you could eat liver, start with chicken. Use lard or bacon grease, brown some onions, add livers cut into small pieces and fry until they are just a bit pink in the inside. Add salt at the end. The texture may seem weird, but it is delicious. I love it with broccoli.