Yheard,
Welcome to the QB forum.
The Singer from 1886 will be fairly simple to refurbish. Most likely it will need lots and lots of oil.
The H/C moves but nothing else does?
Try this: Tighten the stop motion knob on the hand wheel. It's probably been loosened to wind a bobbin then not tightented up again.
The Singer 501s are the top of the line machines for their vintage. They are very flexible as to what they can sew through.
They are however maintenance critical. They are oil hogs and need grease in some places too.
Other than the smoke they can be related to the old steam locomotives.
On your machine start by opening it's manual to the maintenance section and read it thoroughly. If you don't have a manual go to Sears ...... "groan", I have no bookmarks set up yet so I cant post a link. They have free .pdf downloads that print out very nicely.
Joe