for civic 2004 model, its pretty simple.
For best fuel economy, use 5/30 with ci as 5K.
For longer ci, use 5/40 and change it after 8~10K. but change the both filters after 4~5K for better performance.
Good oil companies can be LM, PTT, Kixx, ProfiCar, ZIC.
10W, 15W & 20w oil doesn't give good fuel economy in gasoline engines.
But if still want to use 10w oil, then better choose LM MOS2, 10/40.
Or you can also use LM Molygen 5/50. Its fully synthetic and ci can be upto 8~10k for you car. But change the filters in midway.