Okay, so you are looking for:
- Dual Purpose
- Go Broody
- Meaty
- Protective
- Reproduce fast
In all honesty, I do not believe you can achieve this with one breed or hybrid. My best bet for you would be to keep several broody/lower production birds (wyandottes, silkies, cochins, brahmas, orphington) to be the "incubators". Your rooster should be an EE (which is the "middle breed" which lays good, smaller to medium sized and sometimes go broody) or a gamefowl (which lay poorly, but are great flock protectors).
And then, the rest of the flock should be the layers, the ones that breed and reproduce with the EE and Gamefowl. Should not be a RIR, leghorn, sexlink, etc. Which do not go broody and are sort lived. Why? Because they were bred to just be egg layers and to be switched out often. I would choose a breed like (EEs, ameraucanas, marans, etc.)
How many chickens are you going to start off with?