Cleaning anything you touch constantly is going to be an ongoing endeavor. The moment you touch it again, it starts getting greasy. Keeping your hands clean helps a lot.
I like to start the day with a very clean screen and wiped down outer case (mines smooth plastic). I've found that if I never wipe it down, the whole thing eventually gets so greasy that you're tracking oils from all over the device to the screen - screen gets oily very fast.
So what I found worked for me to help keep the screen cleaner is to wipe down the CASE with a small alcohol pad (sold in drug stores -1" squares) each day. And every morning or before turning it off for the night I'll wipe down the screen with the steam from my breath & a big microfiber cloth- so a clean phone greets me the next day. During the day, if the screen gets smudgy, I just wipe it on my cotton shirt. May breathe some moisture on it first before wiping it off.
This seems to work well for me.