This one is either a 66-1 or a 66-4 Singer with Red Head decals. It could use back clamp feet or low shank feet.
The decals look to be in pretty good shape.
The serial number is located where the red arrow is, and probably starts with "G" I would put some sewing machine oil on a terry cloth and rubbing just the brass plate or maybe just oil it and let it sit before wiping off.
[ATTACH=CONFIG]571546[/ATTACH]
Janey - Neat people never make the exciting discoveries I do.
You can get a replacement plate at
http://shop.sew-classic.com/Slide-Pl...-192-32569.htm and if no manual you can find one at
http://www.singerco.com/support/instruction-manuals Just put 66 in the search box and I think they might have a few one of which might be 66-1. Any of the 66 manuals will show how to install the bobbin cover.