Its best to get the Honda automatic transmission fluid as its neither ATF or Dexron III and running the wrong automatic transmission fluid can mean a quick death to your gearbox.

As far as the oils go... anything between 10w-40 and 20w-40 should be OK in summer. If you're living in the southern states NSW, Vic, Tas, etc... 10w-40 will give you protection in bellow zero conditions. where 20w-40 won't give you as much protection in colder conditions.

Your engine is starting to get a few kilometres on it you might actually consider a thicker oil like a 15w-40.