I recommend a non-oily cleansing water.

This is The Saem Healing Tea Garden Green Tea Cleansing Water. It comes in Green Tea and Tea Tree varieties, and I alternate between the two depending on my mood. It costs around 5,000 won and isn't oily at all, so even when used as an eye remover, it doesn't leave a film or sting my eyes, leaving them feeling soft and matte. It is also gentle on the skin. If you are a beginner curious about cleansing water, give this a try.