Due to it's being popular mainly in europe the 16 is expensive and sometimes hard to find. It's a great choice but probably not for a beginner.
Again, I'm not sure where the notion of expense comes into play, at least for pump action. Check out the manufacturers' sites. 16 gauge guns have the same MSRP as their 20 gauge counterparts (12s are sometimes ~$50 cheaper). The gun shops I've been to don't discount the 20 any more than the 16 -- so the street prices seem to be the same.
Similarly, go to Cabelas.com or Bassproshops.com and look at ammo prices. A box of 16 gauge shells cost the same as 20. At my local Sportsman's warehouse, 16 gauge shells are the same as 20 and 12.
I just don't see where $$ comes into play at all. It sounds plausible -- much lower volume of 16 gauge made and sold would seem to indicate a higher price. Logical. That's not how it plays out, though.
The real issue is availability of loads. This is the big one. There is an infinite choice of 12 gauge loads. Probably 50-75% of these are also available for 20 ga. But, a scant few are available for the 16. As mentioned by others, you won't be able to get shells in a bind -- probably no one you're hunting with will be using a 16 gauge, so forget borrowing shells. Smaller shops probably won't carry any 16 gauge ammo. Etc.
Other than ammo availability, I don't see any reason to select 20 over 16 -- though that is certainly a good reason. Don't see any reason why a 16 is less suited to a beginner than a 20, other than recoil. Perhaps a .410 or 28 ga is a better youth shotgun for recoil reasons. Granted, you're right back into the ammo availability issue that plagues the 16.