For second hand machines you have the option of going to a sewing machine retailer that sells trade ins.
If you want an inexpensive limited number of stitches to do the heavy work you suggested, I would recommend that you get a mid century machine (prior to electronics). People rave about Singer 15s do do free motion quilting. You could buy a Singer or they were manufactured in Japan from the same design and sold under many names. If you get a picture of one, you can just compare them.
I would shop your local craig's list online, local resale stores such as Goodwill or Salvation Army. There are lots of them out there so you shouldn't have to pay and arm and a leg.