Oil: The best thing you can do for any engine is to change the oil regularly. Nearly all modern oils (both organic and synthetic) contain detergents that become less effective over time. Don't be fooled into thinking a synthetic oil can "last longer" or you can go longer between changes just because the oil is synthetic. Bottom line? Doesn't matter if you used organic or synthetic, just change it per the manufacturers recommend interval.
Fuel: If your mower runs fine on regular unleaded, and the manufacturer recommends it, then use it. No reason to switch to a high octane fuel if there's no issue with knocking or premature ignition in the engine. Now with that said, *some* higher octane fuels do contain less ethanol. This is a good thing for small engines. Higher concentrations of ethanol can cause the fuel to break down and debris can form inside the fuel system, usually in the tiny bits of the carburetor. When this happens, the engine can surge or only run smoothly when choked. This can be avoided by treating the fuel with stabilizer to lengthen the life of the fuel. A small bottle of stabilizer can prevent costly carburetor rebuilds or replacements in the long run.
-Robert@Honda
Caveat: I work for Honda, but the preceding was my opinion alone.