Errand runner easy on gas

I think you may have already answered your own question although given your maximum price a used Honda Fit might be a little difficult. A used Honda Element might work. They're not pretty but you can get one with FWD and they're incredibly versatile when it comes to hauling stuff. A Ford Fiesta hatchback might also be woth a look but if you're looking for one with an automatic I'd avoid anything older than a 2013 because many of the early models had transmission problems.
A Toyota Yaris hatchback might also work but I would recommend you drive one first because some think they are underpowered although I don't think so.

The Chevy Sonic Hatchback is right at $6,000 limits. I like the lower hatchback lift over height compared to cuvs.

If you want AWD the Chevy Trax is newer and might not be below $10,000 in the US. The Trax has been on sale longer in Canada longer.