Looking again, a Mazda3 or Civic Si is out of your $6000 reach. However, you could find the Mazda 3’s predecessor, a Mazda Protege5 for that price. But it will likely have 100K+ miles on it. That’s probably the most fun to drive.
I think a Focus ZX5 hatchback or wagon is your best choice; great to drive and depreciates faster than the Mazdas. And that wagon holds a LOT of stuff.
Other choices are a Kia Spectra5 hatch, Suzuki Aerio hatch, or a high mileage Toyota Matrix. None are as enjoyable to drive as the Protege or Focus, but compared to a truck…
Stay away from any VW old enough to be only $6000. They are all pre-2005 and you don’t want to roll that dice.
Unfortunately, a lot of great hatchbacks have recently hit the market, but the selection is really limited for the years in which you will be shopping on your budget.