How to figure out where is the best place to store homemade cookies: in the fridge or on the counter, in an airtight container or elsewhere
If the cookies are baked, I cool them completely. Then, I put them on a plate and under a cake dome. They look nice, don't get smashed or crumbled, keep their flavor, and maintain their texture for a few days. 

I do not store baked cookies in the refrigerator because I have had problems with the cookies becoming dry (even in an airtight plastic bag). 

If I don't need to bake all of the cookies at once, my best results come from freezing the cookie dough and baking on demand. 

I mostly bake chocolate chip or sugar cookies. So, my answer is based on those types of cookies.