What you have is a common 15 class clone. I don't think I've ever seen one with the Kenmore badge on it. The JA36 actually indicates it was built by Riccar, not Maruzen/Jaguar. This is a mid 50s clone going by features such as the striated face plate and the feed dog drop. I have two clones that look like yours, including similar decals. One is badged as a Brother and the other one is badged as a Morse. This machine takes common low shank feet, no need to look for Kenmore specific attachments and it most likely would have originally come with the generic HA1 manual(most clones did) so you're good to go there.
Cari