Keeping screen clean
3M microfibre is the best way to clean the screen and body of oil, smudges, etc. Does not need any chemical or moisture, as the shape of the fibres is what does the cleaning.
To keep the screen clean, Capdase makes a matt screen protector. The matt surface reduces light transmission a bit, and when reading small, fine fonts, you can see the matt surface slightly. i.e. not as clear as with a clear screen. It is workable, though.
On the plus side, finger sliding motions are very smooth, and it does not collect oil smudges from your fingerprints. I've used it for about a week, and have not needed to clean the screen at all. With a cheap clear protector, I would need to wipe it every chance I got, or just get used to the smudges.
So there are ways to resolve the problem, and no, not all screen protectors are created equal.