I always found when painting eyes was to paint it black then add the white eye part around it. Easier for me that way and ends up looking less derpy lol. But decent first attempt.
This was actually taken a while ago (reposting my OC from Reddit) but honesty painting my eyes havent gotten much better haha. Toothpick is a good suggestion!
I use a "hack"; paint the whites, and then once dry use a micron pen (the insanely fine tip ones) to "paint" the blacks. Squidmar on YouTube has a video on it