I'm no expert but, I'd say it's a Singer model 66... and it's a "Red Eye" (the decorations look like red eyes... some are missing on your machine)
with back clamping feet - which are not real abundant but it is possible to find them....
use oil on the moving parts and singer grease (available at wallyworld) on the gears...
that machine should purr like a kitten... 8)
if you are a member of yahoo, there are two groups you might be interested in:
vintagesingers
and just plain
singer
both at yahoogroups.com
Both forums have these great guys who were Singer dealers waaaaaaaaaaaaay long time ago and they can answer all kinds of questions about your 'baby'... and can tell you how to clean the machine etc
also some folks who have replacement parts, etc etc
lots of resources on the 'net too