A used Bernina might fall within that price range. Bernina machines are known for beautiful stitches, especially for FMQ. I have a big Janome and bought a used Bernina specifically to do FMQ and it does excellent work.
A Bernina 150, 155, 165, those are the models that might fall into your price range and they do excellent FMQ. You'll have to ask a dealer or check on eBay to see what they look like and what they might be going for there.