>This may seem like a silly question but if I succeed with raising some queens, what do I do with them all if I can't sell the extra queens I have that I don't need?
Bank them.
> I have some spare nuc boxes but do I just put the queen in the nuc box by herself until I find a place for her
No. She will die by herself in a very short time. Probably a day or less.
> or could I just place her in a cage, in the nuc, and shake some young bees in the nuc with her for a few days before releasing her to start a brand new hive?
Yes, if there are young bees they can take care of her. But is she mated? If she is, then she's already in a mating nuc anyway isn't she? Can't you just leave her there?
http://www.bushfarms.com/beesqueenrearing.htm