Singer model 327K
I found a similar machine at one of those permanent yard sale situations. It is a Singer model 327K made in 1964. It has the single zig zag cam like yours. The foot peddle and power cord are hard wired to the machine. There was no case with it but it would have shipped with a one piece cover that clipped to the ends of the bed. Its a low shank foot and class 66 drop in bobbin.