Help with Selection of New Mower

I'm moving to a new home in 5 wks. Property is about 3 acres, 2 acres mowed. Entire lot is about 250 yards long with about 2 to 3 % slope and fairly level side to side. Quite a few trees and a pond at the bottom with a dam to mow.
I need to mow and possibly do some light to moderate towing such as dump cart with some rock, dirt, wood, etc.
The budget I wanted to stick around was $3000, but it appears I may need to go considerably higher.
The manufacturer's literature states that ZTR's are primarily for fairly level ground and my own research suggests these transmissions aren't too good for anything but level mowing until you get way more expensive.
I don't wish to spend a fortune but can go up some if needed. I don't like the idea that I'm always on the verge of damaging the transmission(s) with even light towing or hills.
ZTR or Tractor would be fine. Any ideas for specific brands or type of machine that would do the job and yet be cost-effective.
Thanks for your help.

Your lot would be fine for a ZTR with that slight of a slope. >15 % slopes start to be extremely problematic for ZTRs or any mower if you mow along the slope. If you choose a rider over a ZTR, get the biggest deck you can get, likely a 52" or 54". A ZTR will save you time, so you might be able to get a 42" or 48" and still require about the same amount of time to cut. There are plenty of options under $3,000 for you out there regardless of the type you get.

Agree that 2 to 3% is fairly level ground and shouldn't be an issue with any mower. I'll defer further comment to those with more experience with units in that price range.