I cant comment on the Davis Mark III, but I was self taught on Davis Mark 15 and their Artificial Horizon. Although the Davis Mark 15
(and 25) takes a lot of criticism for its "plastique" composition, it is a good little instrument, and not any less accurate than my Astra IIIB
at four times the cost. With the Davis Mark 15 and their artificial horizon, I was able to shoot positions to within a 1/4 to 1/2 mile of GPS - well within a landfall sighting.
As far as teaching publications go, there are a lot out there, most of which will have you cross-eye and tearing your hair out shortly into them. The best I found was Andrew Evens' "Step-by-Step Sextant User's Guide"
. In it, he demystifies and simplifies the whole process.