There are youth special permits, most of which are antlerless only.
I don't know of any places that are restricted to youth hunting only but there may be. Someone else may be able to answer that better for you.
As far as special permit versus regular deer license...quality permits are usually timed in such a way that they correspond with the rut, or migration, or some other aspect that makes the hunting better. If I were you and I was getting into the permits game, I'd be applying for both quality and youth points to start building points.
Something else you might look into is a 2nd deer permit. Usually easier to draw, antlerless, in an area where WDFW is trying to manage population issues... ie there are a lot of deer. Note on this that the 2nd tag will cost you about $40.00 if you draw it.