Totally depends on the type of cory you have. The emerald ones (that aren't actually corydoras) can get pretty large, but most of the more common types stay around the 2 inch mark. Some stay small, panda cories and pygmy cories stay under/around the 1 inch mark.
IME corys tend to live about as long as other freshwater community fish, several years when taken care of properly, fed a good and varied diet, good water conditions etc. I have some corydoras that are now about 3 years old.
Musts...lets see. Corys need to have clean substrate, just like other bottom dwellers they can get bacterial infections etc if you dont keep their area clean. They actually need to be fed, they dont just clean up leftovers. Mine love shrimp pellets and all of the usual food I feed my tanks (flake, bloodworms etc). They also need to have pals. The more the merrier. At least 3-5 together.