The big thing with the oil is to make sure it does NOT have the 'energy conserving' mark on the label. Yer clutch just won't like that.
Now while you can use automobile grade oil in yer bike, all the little additives in this type of oil can't take the abuse that a bike engine and clutch put out. General consensus seems to be that at about 500 miles you can start to get oil breakdown.
A motorcycle grade oil is what you want, but, a caution here also. You'll run across containers that state they're formulated for v-twin engines. And they are. For AIR cooled v-twins. Ya don't want that. Yer machine is liquid cooled and has different characteristics.
Now, with my machines, both my '05 X and my wife's '04 Aero, I switched to Amsoil at 600 miles. Gotta say that both bikes operate smoother, cooler and with better clutch response than with dino oils. On my '04 X,I switched at 9000 miles and had a noticable improvement in my bike.
Just a side note here. A lot of folks like to change the rear differential oil when they change the engine oil. It seems that Honda has an additive in this oil that is necessary for proper break-in of the differential. So, again, general concensus is to not change that oil till the first change listed in yer owners manual.