You might be able to find an old Kenmore for less than $100. They're really a great old machine.
The problem with new machines under $250 is that they usually have pre-set stitches (there's no control over the stitch width), and they're not very well made.
There's a Bernette 15 that has control of the stitch width, metal oscillating hook (bobbin system), buttonhole applique stitch and buttonhole system for about $270.