I use an STP extended life 2808 because of the silicone anti-drainback valve, which I consider the most important part. Most 'synthetic' oil filters have that too. STP kits just happen to be on sale at AutoZone pretty consistently these days.
Honda recommends 5w30 for all temperatures, like mentioned above, or 10w30 if you don't drive in freezing or colder weather.
These engines don't require synthetic oil, so you can use conventional if you want. I use synthetic, but that's also because it happens to be on sale at AZ with the filters I like.
DO NOT WAIT 10,000 MILES TO CHANGE YOUR OIL. The built in maintenance minder (if reset properly) will turn orange around 6,000 miles, and red around 7,500 miles. Regardless of what oil/filter you use, always change your oil at least that often. 'Extended' service intervals are what damage engines, not low quality oil. No oil lasts 10,000 miles if you want the car to last.
Also, it's good practice to rotate tires, and inspect brakes, suspension, bearings, exhaust pipe, underbody, hoses, wiring, fuel lines, etc. at every oil change. I have saved myself from part failures by doing regular inspections.