I use "camera lens style" microfiber cloths, they can be brought up to 30cmx30cm size and are very easy to wash and dry. And my solvent of choice is good old solution of distilled water and IPA in ~70/30 ratio almost always, and 50/50 for stubborn marks, and 100% straight IPA for very tuff dirt and marks-although straight alchols significantly increase odds of scratches. You can use plain water, but it has very small dissolving power and the added IPA just gives it a huge kick.
You can use tap water, but being a perfectionist I always use home brewed distilled water. Using any kind of tap water which is loaded with minerals on glass is a bad idea longterm, as minerals like calcium are notorious for building up on it. So all glass I use distilled water and my IPA is also filtered through ultra fine 0.01micron mesh filters as the containers come with containment in them. Mineral build up is like plaque on your teeth, it adds a furriness to the surface and just feels awful.
I use to use those really meaty detailed towels but I soon learned they are nasty and induce fine scratches. The problem with MF towels/cloths is they are made of microscopic shards of plastic, and plastics require plasticizers to keep them soft, but over time they tend to evaporate out and the fibers tend to bunch up, all which makes the strands more likely to scratch. The other three big factors that causes scratches is any kind of movement between the cloth and surface, excessive force, and of course any debris in between cloth and surface. So to avoid this I try to use the padding technique which drastically minimizes scratches but takes alot of finesse. This involves gently pressing the wet and dry cloth but is very inefficient compared to wiping motion. I do this all the time on Chromium plated stuff, as with conventional rubbing it will eventually scratch. Flooding the surface with solvent mitigates the risk from debris but must be done with caution as moisture/water can get in places you dont want-like the edges of the screens.
Scratching results because the surface is too hard and brittle and lacks toughness and flex. It may not seem like it, but at the microscopic scale a tiny pieces of cotton/plastic fiber is backed by your hand with a huge force and in such a focused spot, its a bit like rubbing a fork aggressively on a DVD. Glass is very hard and very bad, once its scratched you can never remove them. But synthetic materials and coatings are better at resisting it, but usually impact the optical transmission slightly. Raw glass can be polished to clean any stains and marks which will not scratch the glass, while other synthetics and coatings usually are too thin.
Glossy screens are much more vulnerable to scratches than matte screens, and some matt screens (most I have owned) usually are sacrificial, meaning they lend themselves well and don't scratch easy, the surface tends to wear down hiding it. I have used to this to "buff out" small imperfections in the actual screen of many refurbed screens, instead of needing polish.
I can say that all the dozens of screens I have owned and cleaned dont mind occasional 100% IPA, thinkpads could care less. Just don't let too much of of it or any water near the edges as it can diffuse in under the other layers. Metho and Ethanol are too aggressive unless heavily diluted in water.
Finally I shouldn't have to remind people of how truly insidious dust is, even on a vertical surface. To deal with it I gently run a dry clean MF cloth along it a few times every 1-2 weeks. yes this may very well add fine scratches overtime, but thats life.
