Homemade diets are best left raw, or mostly raw.
A quality kibble will have minimal ingredients and optimal nutrition. I feed my dogs Taste of the Wild, but I have fed raw and BARF-style diets and if you have the time, dedication, and resources I think they're great diets when done appropriately.
First things first though... Don't feed those table scraps anymore! Ground beef, fries (greasy and salty!), and things like that definitely don't belong in your pittie's tummy. A high-quality kibble is SO much more healthy than the foods we put into our own bodies. I personally recommend Taste of the Wild or even Tractor Supply Co's 4Health Grain Free kibbles.
I make dog treats for my training clients, if you want some recipes I can send them over your wayAs far as the diet goes, however, in your situation I think it is best to choose a high quality kibble.