I know this is a basic question, but what is the best paint finish for a playroom/basement? I heard flats are better to touch up and eggshells are easier to clean. Any advice?

For a playroom I would say go with the eggshell. You'll probably get more mileage out of the cleanup feature. Your touch ups are bound to be dents and dings rather than just scuffs.
-Dan

We did our daughters room in a pale yellow semi-gloss finish. My daughter went thru this drawing on the walls stage and those walls were by far the easiest to clean.