Microfiber normally. If it's a stain, water with a damp cloth usually gets it.
Vodafone Germany also recommends on its websites microfiber cloth for cleaning smartphone displays:
"
Clean and disinfect the cell phone: What you should do - and what you should not do!
You don't need much to clean your smartphone: a clean, dry microfiber cloth and a soft toothbrush are sufficient for most dirt.
What you absolutely do not need is disinfectant, glass cleaner or washing-up liquid. Most of these cleaning agents are much too aggressive for the smartphone and can attack the surfaces. Displays, for example, have a grease-repellent coating and this layer can be damaged by aggressive cleaners.
If there is an important reason why you want to disinfect your smartphone properly, this is possible in exceptional cases. Cleaning sprays with an antibacterial effect for cleaning touchscreens are commercially available. You can use such a spray to disinfect your cell phone. But you should only do this in an emergency (or very rarely), because even these special cleaners are not good for the surfaces if used frequently and with long exposure times.
This is how you proceed with a thorough cell phone cleaning:
The protective cover: If you are using one, you should take it off and clean it separately. Over time, a lot of dirt collects here: fat and small crumbs settle on the edges. How you can clean the cell phone cover depends on the material, of course. Careful wiping with a clean, damp cloth should be no problem for most materials. Simple plastic or silicone "bumpers" can even be cleaned under running water and with soap.
Your Smartphone: With the microfiber cloth you can easily wipe the surfaces of your cell phone. Openings for microphone, speaker, USB-C or Lightning port can be cleaned carefully with a toothbrush (which can also help with charging problems). But you should not exert any pressure, because otherwise the microphone can be damaged.
Stubborn dirt can be removed by moistening the microfiber cloth. Of course you should be careful when handling water: the cloth should really only be slightly moist, but not wet. It's different if your smartphone is waterproof - then you can even rinse it. But even then, you should avoid cleaning additives like soap."
(Translated from German by me)