Based on that, one very common machine to study up on would be a Consew 206RB5. There are tons of other machines in that range that are almost the exact same. Singer 111W, for example, to name just 1. Most will sew up to v138 thread, some 207.
With some luck, you could score a used machine in the $500 range. New, you'd be about 3+ times that.
Plenty, plenty of other types and styles of machine would fit your stated need. This is just a suggested starting point to maybe focus your search.