The first thing to do is to get some quality face paint.
I recommend going to a theater supply store - you may pay more
at first but a little goes a long way and the results will be well worth it.
And you know if the paint can stand up to the hot stage lights of Broadway it will be fine for a baseball game.
I've had good results with Kryolan Aqua Color - and it comes off with soap and water making removal easy.
Just make sure you mix it well before you apply it - if it's too thin it will run down your stomach (and sometimes get
on your clothes).
You'll also need some quality brushes. Again, this is no place to skimp - the cheap brushes just don't do a good job. Get 3 brushes - a large one to cover area quickly, a medium one to fill in smaller areas - and a small one for the finest details.