I know this is a little late but, Honda recommends using 10w-40 that are not labeled as energy conserving. Most all oils sold at any auto parts stores are energy conserving oils and contain chemicals that could be potentially harmful to the engine and transmission. On the back of the bottle there is circle that contains a API rating, it should be SJ, SAE 10W-40.
In the engine side the I would recommend Honda GN4 convential oil (black bottle), Honda HP4 non-moly synthetic oil (gold bottle) or Honda HP4M moly based synthetic oil (silver bottle). I have used HP4M since mine was new.
The engine should be refilled with 690 ml/cc of oil after a drain and filter change or 660 ml/cc with a oil change only. The oil should be checked 3 min after the engine has been turned off after warming up. It should read about 2/3 up the dipstick, this is just right (it leaves enough room for the oil to expand while running hard and hot).
The check screw on the side of the transmission unfortunately can not be trusted. Oil will run out at about 500-550 ml/cc and will leave the transmission low. You will notice a whine in the middle of the rpms and up. This is the kickstarter and idle gears spinning under lubed. The trans requires 600 ml/cc of oil. I run mine about 625-650 ml/cc. I would recommend Honda GN4 oil or HP4 non-moly synthetic oil. You can also use Honda HP Transmission fluid (red bottle 85w-90 High Performance Gear Oil). I use the HP4.
You don't have to use Honda chemicals but, be careful what you do use. Some automotive oils use "slickeners" to enhance their performance and will cause a wet clutch to slip. Don't use the HP4M in the trans, it contains moly (slickener) that will ruin a clutch but is good for the crank. I would not recommend normal automotive trans fluids either, they mostly are thinner hydralic fluids that are made to pass through tight passages and valve bodies while still lubing the gears. Trying to get out cheap could cost a lot more that $16 for the right oils.
Service Honda Engine Page