My Janome 6600P has the start/stop button as does the Babylock Espire. I love both machines and I think you could pick one up within your budget, as they aren't the newest model. The Espire has an auto foot lift for appliques, which is why I purchased it, but I'm sure there are more machines out there. These are just the 2 I can vouch for. Good luck and your story is inspiring ;-)
~ Pat