Are you wanting a large harp space to piece the quilt together or to do the quilting after you piece it together? I have a very small vintage machine with a small harp (called a Featherweight) that I have pieced king sized quilts on. But I would never consider quilting a king on a small harp machine. It is when you do the quilting where you need a large harp machine.
Since you already have a Babylock, I would suggest looking for a good vintage machine. I use a vintage Singer 15-91 for my quilting. I have done twin and queen sized quilts on it. Try looking for videos on YouTube on quilting with vintage machines if that interests you.
If you want a computerized machine, I would suggest either a Brother or Janome in your price range. I have used both in the past and have been pleased.
Good luck with your decision and let us know what you decide! Welcome to the board!