You should NEVER wash-down a mower , use an air-hose or blower to get the dirt off, then a DAMP rag, be especially sure to keep water off the cutting-deck ( they tend to trap water ) and mowing wet grass is another NO-NO ! ( lawn service companies are stuck into doing it at times but I'd say most avoid it, if at all possible ) and most of those outfits take GOOD care of their money-makers !
I think the MOST important things are to be sure you use super-clean fuel containers, change the filters, and ALWAYS, ALWAYS ..CHECK and change your oil levels ( don't forget the Transaxle(s) once in awhile ! ) RUST NEVER SLEEPS !!