If there are a lot of hills you will need to go with one of the mower, or better still garden tractors with a horizontal crank engine.
Garden tractors have a lot stronger transmissions than mowers so they handle hills a lot better, last a lot longer & usually have an external replacable filter.
Horizontal shaft engine can happily get tipped 45 degrees with little damage, do that to 3/4 of the vertical shaft engines and it will be good bye crankshaft.
Really rough ground dictates a fabricated deck or at least a very heavy pressed deck.
SO look for a 3000 series cub cadet but if you get one of them also look for some spindles as Cub discontinued support for these mowers in 2015.
Thus commercial users began dumping them, The 2000 series are also really tough but the decks are not as heavy as you would need thus require regular panel beating.
Then there is the Bolens GTX / Troybilt Duratrac there are thousands of them out there at less than a grand.
Again a downside is that Eatons no longer support them as they got out of mowers all together because they refused to downgrade their product to a price that mower makers would pay.
However because there were so many there is a lot of aftermarket parts and a couple of single model specialist who make parts for them.
Good side is I see them with anything from 5000 hours to 36,000 hours ( when the meter stopped working ) still running like a top .
Then there are the Hondas, Honda got out of tractor style mowers back in 1997 ( for the same reason as Eaton ) yet there are thousands of them still running strong, I have several in my service run & you just can not kill them.
Do not expect to get a pristine mower for the money you are willing to spend and be prepared to either live with a few niggles or do some repairs yourself.
The bonnets on most mowers is simply cosmetic so do not be afraid of buying one without a bonnet and they tend to go cheap.