Some of the early manuals actually list a number for the Attachment set. I got a compiled list from the Vintage Attachment Yahoo group - I think it was compiled by asking - However you can have two sets that are exactly the same with different numbers on the box. Most of the boxes I have - the stamped number has faded so it's no readable anymore. Some very early ones it was stamped. HOWEVER, I also would not put it past Simanco to have a number that is for the BOX and has nothing to do with what gets put inside - Simanco put numbers on each componenet part, and then gave the complete unit a different number that wasn't actually stamped on anything . . .
The best way to know what attachments should go with your machine - find a date appropriate manual and study the attachments shown. if you don't care about getting period appropriate ones, then except for a few cases, they all fit everything.
The early basic set that came in the green box included
Tucker
Ruffler
Narrow Hemmer
Adjustable Hemmer
Binder
Edge Guide
Bias Cutting Guide
Large/small screwdrivers
small stiletto
in the 30's, the Tucker and edge guide were removed from the basic set, and the Edge stitcher and gather foot were added.
The Ruffler went through several changes until it got to the 4 slot style. The Adjustable hemmer had one change so the arm could swing out of the way instead of being removed. The binder also went through several modifications, no slot, single slot, multi slot, multi-slot with guide pins.
Prior to the advent of the 66-1, there are a lot of different attachment sets - the 66-1 came with a special set, in fact there are at least 4 different sets for the 66-1 depending on year of Mfg. Probably around 1915 (about the same time Singer switched to the small green manuals) this got a lot more standardized. The 101 came with an extended set of attachments. Attachments saw more changes with the 400 series.
My most recent fun has been compiling a list of Singer Domestic machine manuals - and next will be to build a collection of them.