Don't assume the manual that came with the machine when you got it - was the original one that came with the machine. I've learned that the hard way!
And so did the person I bought a white FW from. It came with a manual for a 66 . . . she did her research, and was FIRM at $75. I did not realize what happened until after I'd paid, and she was commenting on how nice the manual was, and I casually said it had nothing to do with the machine, and I didn't have a use for it.
About half the machines I've gotten did not come with manuals, of those that did, about half came with the wrong manual (either wrong model or wrong series).
The threading in you picture and mine are the same - only the faceplate is different. The only thing you have to be careful of with 15's (and this is pre potted motor) is that for a short while Singer changed the 15 - and then they changed it back. I don't think it affects anything except the bobbin case is different.
When looking at covers of manuals, there will usually be a REV (XXX) number under the Form number, that is the Date of the revision, so (428) is April 1928 and (1032) is October 1932. Helps to locate a manual that is a revision slightly earlier than a machine date.
Example - your machine was made in 1928, you really don't want a manual with a revision date of 452. That mistake is one reason I've got some extra manuals - I bought them before I realized there were so many revisions. However it is interesting to look through them and see what changed - on one, it's only the light that came with the machine.
I have a manual for the 15-88 & 89 rev 336. It shows the scroll faceplate but not the smaller pictures showing the tension and needle. Pages 12 & 13 use the same drawings, but the wording is slightly different as is the type font.
From looking at them, if Singer made some serious changes to the booklet, they changed the Form number. If there is no revision date, then it's the first and you have to look at the copyright date to help figure it out.