An average half acre yard can be mowed in one hour with a regular push mower 21 inch. However it can get a bit tough after the heat and humidity of summer arrives. A bunch of good ideas have been dropped for your consideration. Here is one more. For the money you say you can provide about five decent average mowers can be purchased brand new. At least three much nicer ones can be purchased. Consider a pair, you always have a backup if the one is in shop for warranty work. Or buy an upper end machine and a lower one, still always have one for backup. If you buy a used machine or a new lawn tractor in your price range you are going to need a backup anyway for possible shop time. Another thing to consider is to just buy one 300 to five hundred dollor machine and keep some cash for a purchase of a backup if you ever need it. One hundred fifty dollors is alot easier to come up with on short notice than five hundred or a thousand for minor to somewhat serious repairs. A cheap mower to do an acre can be had for one hundred fifty to get a person by. If you are still healthy a cheap to good to great quality 21 inch mower will get you by just fine for one half acre. Very little to maintain, very little to go wrong by comparison, less filters, less stabilizer, less oil, no tires to puncture, no hydros or steering to wear out, less folks that want to borrow or steal it, easy to take to a shop, easy to put away and forget about it until next season, trims nice around trees, very healthy to operate. Just something different to think about.
I plan on keeping my 18" mower as its not going to be worth a whole lot even though it runs great and has never given me issues. I am leaning towards the 21"/22" mowers, but would still like to hear from others on their experience.