Found that sewing machine mentioned in this article online:
http://www.ismacs.net/sewing_machine...recommend.html
Here is an article on treadle machines that may help you with needle selection:
http://www.treadleon.net/sewingmachi...ngtreadle.html
Most of that genre of sewing machines used regular Singer needles. Size would not be the important issue with a needle, but rather type of needle. Some needles have a flat side at the top that is used to position the needle while others are round at the top. Whether a machine is a treadle or not is largely irrelevant; it's the model type that is more important. The machine you have is probably a standard short shank machine that takes standard Singer needles made for short shank machines. Your machine is likely a rebranded Singer model.
I doubt that the #7 on the needle plate means anything, at least in terms of needle size/type.
Vintage sewing machine groups and treadle sewing machine groups will be of help too.