I have several bags in my freezer. One is for chicken.... I put in all bones and skin from roasted chickens, all little pieces that I trim off raw chickens when preparing them, giblets and necks, and any fond from the bottom of the roasting pan that I have deglazed.
I have another bag that I use for cooked beef bones, (T bone steak bones are great) scraps from prepping and deglazing liquid. I also add things like the end of the tomato paste can, the end of the stew, bits of mashed potatoes etc. When I find the freezer getting crowded I pull out the bag and start cooking.
If I have enough of one critter, I will make straight broth. If I don't I will mix the bones. My family has referred to this for years as "garbage soup". I think the key to good broth is to make sure a good portion of what you are using is well browned. I will brown chicken necks and even raw skin in the oven if I don't have enough carcasses. I never use meat from the broth stage in the soup. It has already given up all flavor. So if I want meat in the soup I save it separately and add it at the final stage of prep. You can set aside chicken breasts and poach them just at the end to add to the soup instead of letting them get tasteless by hours of cooking.
Also, the best tool I have for soup is my pasta pot. I put all the bones in the insert and once everything is cooked it is a snap to lift the insert for draining. Then just dump the contents of the insert and continue.
Your post was really helpful, thanks! I love your family calling it garbage soup. Your mention of t bone bones made me realize I haven’t had one in forever. I am now saving every single meat bone.