For pretty much any Matte LCDs (which includes the ones you have):
It is best to use a mixture of Isopropyl alcohol + water. The ratio of alcohol to water is entirely whatever you feel like. Some people use 50/50. Others 20a/80w. Sometimes 100% alcohol if you are trying to remove a really stubborn mark. No problem.
Isopropyl alcohol:
A very pure substance. It is the same stuff used in hospitals for cleaning wounds / everything else. So "pharmasutical grade" is the version that comes approved for hospital use. Non-approved version will be cheaper. The main thing you need to realize is that the stuff will completely 100% evaporate away and leave no residue behind. And that's what you want the stuff to do, isn't it? You should therefore buy a solution of 100% isopropyl alcohol that you can reasonably afford. Just ensure that it is pure and not been mixed with anything else. For example secondary cleaning agents.
Water:
If you use tap water in a large component, then THAT can leave a slight whitish residue from the calcium. That would be common linescale, the stuff you see in the bottom of your kettle. Perhaps you happen to live in a hard-water area.
Otherwise if you use bottled mineral water... then the amount of residue will vary entirely depending which exact brand of bottled water. I have no particular recommendation but some will be vastly better than others.
Filtered water perhaps should to be better than tap water (ie black charcoal filter). Getting even better: De-ionised water may be better than filtered water. But "de-ionized" has just the charged ions removed so is not completely pure either. "Distilled" (evaporated, then re-condensed) is 100% pure H2O and definately would be the best. With nearly no impurities. Again, pharmasuitical-grade distilled water is also available too and would "guaranteed" pure. And of course that is also the most expensive kind to get hold of. So Just get the best kind of water that you can reasonably afford. Remembering that the worst thing is it will do is to deposit a slight residue.
Most things (apart from acid) are unlikely to will damage the plastic itself of the screen. So applying some other common cleaning agent is usually OK. For example vinegar or other more common types of alcohol like the purple methylated alcohol, or "white spirit".
There are also many dodgy "no-name" / unbranded LCD cleaner solution. They are suspect from the perspective that they nearly always don't disclose on the label any of the chemicals it has in it. So there's no way to tell, and can be a waste of money. Similarly, for most such products the worst thing they will do is leave a residue and / or not be very effective. They tend to by more on the side of the solution being too weak to do anything. Because then they can't be accused of selling something that will damage the screen. It just won't clean it either!
Finally. Its also possible to buy one or two reputable "LCD cleaner" where they DO disclose what the solution is made of. Those ones should only ever contain 2 ingredients: isopropyl alcohol + distilled water. Then you are just paying a premium for letting them mix up the solution for you (in whatever strength they chose it for you). The main advantage of buying these 2 products seperately it that you can start off with a weak solution and if that failed then mix up a stronger solution with more alcohol in it to try again.