I'd stick with a Briggs & Stratton Engine because the parts are cheap and readily available. I've got no experience with Honda engines, but I would expect them to be more expensive and harder to repair at this point and time. (maybe better in the future if they gain marketshare in the mower industry)
Stay away from Tecumseh engines. They're priced about the same as B&S, but I've had 2 of them that only lasted a couple of years before they started having problems. Most of my B&S mowers in the past worked fine for at least 5-6 years without major issues.
Toro and Snapper are both good, but these are higher-end mowers that you'll pay extra for...just keep that in mind when you're shopping. Sometimes buying a standard mower with a 20-22" deck and a B&S mower is the best way to ensure that you'll be able to maintain it without a lot of headaches.
Tips: When you get your mower, keep the blades sharp and clean the mower deck by scraping out the hardened grass that builds up in there. Just keep in mind that you don't want to turn the engine over or on the side facing the exhaust...this causes oil to leak into the exhaust...not pretty.
Happy Mowing.
