With only one acre of lawn I'd say you could easily get by with a Wally World special. Namely one of the larger Yard Machines with a pressurized oil system engine. People really bag on the cheaper machines but with a little care they'll easily last over 20 years as long as you don't abuse them. If you are truly mowing lawn that isn't infested with sticks, rocks and small trees a lighter machine will easily handle it.
My MTD is a 18 HP model sold by Wards in the mid/late 1980s. The previous owner kept great records and mowed over half a block with it every summer until a I bought it. The oil was changed 2 or 3 the times a year and every two years it got new blades. Over twenty years its gone through three deck bearings total. Never spent a night outside according to the owner's widow. Is it as good as an old Cub, Wheelhorse or Deere, hardly, but then it doesn't need to be.