In that case, whatever age they sell is the easiest to start with :)
If they have all ages, then adults would save you the bother of brooding the first ones, but they have a short enough lifespan that you would probably be brooding new ones each year after the first.
Coturnix quail can start laying eggs when they are 6-8 weeks old.
So getting mature ones would not save you much time!
Quail chicks are very tiny, which could cause trouble shipping them through the mail--I tend to see quite a few eggs for sale and not many chicks or adult quail for sale.