When we bought the house we're in, the sellers asked us if we wanted to buy their ride-on mower, and we did. Sears Craftsman. Not sure how long they had it, but it lasted us for 10 years with only a few issues here & there. We have about an acre of lawn, with some moderately steep hills.
Anyway, the Craftsman died last fall, so DH was just out shopping for another ride-on over the past couple of months. He looked at Craftsman again, but ultimately decided the quality had gone down. Ended up buying a John Deere, but he went to a dealer, instead of Lowes. He paid more of course, but he figured he'd get better service from a dealer and the models the dealers carry seem to be a slightly higher quality than the chain stores. He uses the ride-on A LOT, also to pick up leaves in the fall.
On the subject of hilly areas and ditches, you need to be very cautious since ride-ons can slip and/or roll over. You'll want to make sure the tires are good, and there are also wheel weights and other modifications that you may want to consider depending on your hills. Also, if that area is so steep that you have concern, you might want to just consider tilling it over and putting in some ground cover (such as ivy, wildflowers, etc), or maybe mulch with some shrubs. Just a thought.
Congrats again on the new home--hope you are enjoying it and continue for many years to come!
"The number of times you fall down is irrelevant. The number of times you have the courage to get back up is what matters." - Coach Nancy