Sewing Machine Problems: Sears Kenmore Model 1802, Zig Zag Sewing Machine?

Sewing Machine Problems: Sears Kenmore Model 1802, Zig Zag Sewing Machine? I recently was given a really nice sewing machine from the 1970s that had only been used a handful of times. It still even had the original instruction manual with a letter that is addressed "Dear Homemaker" (haha...). The warranty actually just went up maybe 2-5 years ago. It's the kind that flips up out of a table so you can keep it out of view at other times.

Anyways. I know I'm threading everything correctly, I have the tension accurate as far as I can tell, but every time I start sewing one of two things happens. 1) the bobbin (which goes in from the front underneath instead of straight down like what I'm used to) pops out and falls on the floor (even when I've snapped it in place) once I pick up any speed beyond just turning the wheel by hand. Or 2) I get a horribly tangled mess down in the bobbin/shuttle area that causes the everything but the motor on the machine to stop going and often breaks my needle.

Does anybody have an idea of what's going on?
I know the machine works well, because I've already used it to make several items. I had this problem once already and I thought I had fixed it, but then I had to add more thread to the bobbin and the problem came back, so I have no idea what's going on.