and the quickest answer is “it depends”. Very generally, raw meats are OK, cooked meats are OK but can cause some digestive upset. Cooked veggies are OK. Limited cooked grains are OK. Sauces, jams, fruits, dairy products, etc should only be fed sparingly if at all. Raw bones are OK but cooked bones can shatter and cause splintering.
We have done raw homemade dog and cat food for years, and there are recipes you can follow which will provide complete nutrition for dogs or cats. Whether it’s cheaper or more expensive is something of a debate. Yes you can feed costco kibble (or the like) very economically, and that’s probably the single cheapest option unless you raise your own meat and veggies and feed your dogs/cats out of your own garden. But many folks claim that you eventually “pay the price” for cheap kibble, via higher vet bills. We saw our vet bills drop dramatically after switching over to homemade raw foods but it’s not something which I can measure and quantify. In essence, you get what you pay for. Garbage in, garbage out.
I would suggest there are a variety of books and websites that you can read, to learn what’s safe and what’s not, and what is ok when fed in small amounts, and which recipes will give your critters complete nutrition. There are also Yahoo groups which are for folks feeding raw and/or homemade diets, either in full or as a supplement to purchased pet food, to help answer more involved questions along these lines.