Oh, jeez, here we go again with the oil wars...
If you can find oil that has the same formulation as was recommended by Honda when the bike was new, you've found the right oil. Back then, the common additive package was compatible with both cars and motorcycles with wet clutches and transmissions using the shared oil.
However, oil formulations and additive packages of today's automotive use oils have changed a great deal, due in part to the widespread use of catalytic converters and polution standards not in use when the SOHC4s were produced.
Today, common auto oil uses an additive package that omits the zinc that transmission gears benefit from, and sometimes adds moly or other additives which clutch friction discs aren't really compatible with. So, generally speaking an oil blended for motorcycle use will likely add the most longevity and protection to your machine. 10W-40 works well. If you are going to operate with high average outside temps then use 20W-50.
Oh and read the FAQ