I saute the rib meat with olive oil, garlic, and onions first right in a big pot and then put all the other stuff in after. Then I cook it for many hours, sometimes 10+ depending on what I have in there. If I have fresh tomatoes, I cook it longer until they break down.
Why would your family not make bay leaves?
Anyways, one of the easiest and most delicious sauces is a clam sauce. First you partially saute some garlic in a pot with olive oil. Get a few cans of whole baby clams or chopped clams or both, put the clams in the pot with the juice and everything, add some parsley and a bit more olive oil, bring it all to a boil, and then let it simmer for like ten minutes. It's quick, easy, and very good if you like clams.