jengiz-
Congradulations on the new boat, and welcome!
SF Bay is all mud and sand, except for a very few areas where the tide really rips and rocks are exposed, like Racoon Straights, but you probably won't be anchoring there.
Any of the three most common anchor types for the C-Dorys will work in the bay.
The Danforth has a lot of holding power because of the extra area of the flukes, but doesn't re-set itself in a wind or tidal change as well, and won't do well in rocks, should you go somewhere later off the bay. The Fortress variety with it's adjustable fluke angle and mud paws, however, is rock solid in soft mud. Pretty expensive, though.
The Bruce or bruce knock-off is a good all around anchor. It dosn't have the holding power of the danforth in mud, but is OK, and resets itself well, and is good in sand and rocks.
Perhaps the best compromise for your use would be a plow anchor like the Delta Fastset. It works like the CQR, but is lighter and more suitable for a smaller boat, resets itself well, and works well in all situations.
The 9 lb Delta Fastset will actually hold a CD-22 well, and is rated for 9-20 foot boats, and will hold your 16 very well.
Be sure to use at least 10 feet of 1/4" chain between the anchor and the rope rode, as it's the weight of the chain that makes the pull on the anchor horizontal and digs it in. Also, power set the anchor with your motor to get a full bite, not just a surface hook in the top of the mud.
Keep in mind all the above are generalizations.
I don't think you have a chain locker, although a few with 16's have added them-look in Oldgrowth's album for a very clever example.
You can carry the rode and the anchor in a milk carton / case carrier, and take it forward when you need it, or lash it to the foredeck. One nice thing about this system is that it's easy to rinse off the stinky SF Bay mud when you get back to the dock, either on the dock or foredeck.
You'll love San Francisco Bay! And the Estuary! We spent 38 years living in the East Bay, 35 years of it teaching, and over 30 of those racing sailboats in the bay and elsewehre. Good luck with your new fun machine!
Joe.