As a former Small engine tech, I'd have to put my money on John Deere's EZ Track ztr's. The Z225 was hands down, head and shoulders above it's competition. Toro's TimeCutter series would be my second choice. Everything else I've tried or worked on has been disappointing to put it politely.
They're a bit over your $3000 limit but have you looked at 4-Wheel Steer tractors? I think they have more to offer residential customers than ztrs in many cases. Real towing ability (and attachments)and virtually no turf scuffing while mowing around trees. Check out the John Deere X304.