All the Davis I have with the needle on the plate take the 15x1 size needle. The "long" needle is quite a bit longer than the 15x1 needle. This looks like the 3/4 size machine, and if so it may take a shorter shuttle than the full size Davis.
I have a 3/4 Davis machine that takes a full size Shuttle (MN model B) and two 3/4 Davis machines that take the shorter shuttle. In fact, I bought the second one specifically to get another shuttle (machine is very bad shape) as the short shuttles are very rare. Regular size are easy to get.
Davis put lots of different names on their machines - almost as many as National.