Give the undercarrige, brake lines, cooling system,, ball joints, tie rod ends etc. a once over. If that stuff looks ok, a $2K engine is probably worth it. I'd fix any obvious issues at the same time the engine is replaced.

You can't get much for $2K that is guaranteed to have no issues.

Your other option is to spend a little more and get an economy car, even a new one. That isn't a popular option on a car site, but there is a big difference between 16 mpg and 28-30, unless you don't drive much. It's nice to be able to gas and go for the next 5 years after driving worn out junk, too. Again, not a popular assertion on a car site.