Well if you really want to try to graft, then I say go ahead and do it. It will take some time to practice, but no matter what you will learn. Sure you could graft some cells into a five frame nuc, and they might make a cell or two, or even more.What is the minimum I need to start?
will a 5 frame nuc with a few frames be enough to get started? any links? advice?
But if you are interested in making some quality queens then IMO you should have at least 3 hives to play with. One hive to graft from, one hive (should be your strongest) to use as a cell builder, and a third hive to tear down to use to make your mating nucs. You will need a mating nuc for each queen you want to mate.
Now you could graft from the same hive you use as a cell builder, which would mean only 2 hives.
But most folks want some honey too ...
But can you do it with less? Sure!
However like the rest of the gang said, you should start out learning how to do splits and you should have at least 3 hives anyway so you know what is working and what doesn't.
Also don't forget you will need lots of drones too so that is another reason to have more hives.