Also be careful with the flat spring (the thin metal flap covering the front of the bullet shuttle). If this is or becomes bent or bowed, the machine won’t sew right. My Household 3x has the original, but the spring is warped - probably why the previous owner thought the machine didn’t work. I use a Boye replacement and the machine sews well.
And leonf is right. Oil, oil, oil! A Singer may run months between full oilings (depending how often and hard you use it), but never let it get “dry”.
With the long bobbin machines, there should be a tiny cup with a felt or rag (the wick) in it to keep oil on the race (the curved flat track under the slide plates that the shuttle moves against). Each pass, the flat side of the shuttle spreads the oil along the race. The wick needs to be clean and kept oiled. I replaced the rotten wick on the 127 I had with a section of a red spool felt cut to fit snug and about flush ithe the top of the hole.
K