Only machine that I am aware of with the automatic thread cutter in the price range you mention is the Sparrow 30. Perhaps there are others, but I am unaware of them. There are many used machines to be had on Ebay, and if you buy from a reputable seller with Free Returns, it usually works out. But these machines, unless more expensive models usually lack a thread cutter. They may have many of the other features, but seem to lack a thread cutter.
I have bought a couple of machines on Shopgoodwill.com, but one was a vintage singer which was very nice, and the other a Pfaff, which I really like but it didn't come with a thread cutter.
I do think if your objective is getting a machine with a thread cutter, then the Sparrow might be a good choice.