Honda makes good small engines, but for under $300 you dont get their top quality product...so take that honda name with a grain of salt. I've had bad luck with consumer grade newer Briggs motors....especially those on Crapsman mowers.
Just find one in your range, with more HP than you think you need, and take care of it. used 1x/week it should last more than 10 years. I heard the Honda Harmony is a great mower, but the only guy i know that has one had issues. Luck of the draw!
I've had decent luck with a Troy Bilt power washer for about $300 from Depot or Lowes (cant remember). It has a consumer grade honda rated for 300 hrs of use. That's right...they are designed to last for about 300 hours of use. Sure, they might go longer, but that aint much. however, to use it around the house only, you should again make it longer than 10 yrs.You must get a gas-powered unit to make it worth your while. Most will come with a tube to suck up detergent automatically, which is cool.
Good luck