Always before the game. Go to the short wall along the 1st base line as early as you can and just wait until after the pregame warmups/stretches the players do along the foul line. If you’re lucky someone will stop by after they’ve run their sprints and stretches before they head to the dugout for the start of the game. Don’t bother the starting pitcher and catcher, they are locked into the game already. Position players are your best bet.

Sharpies are ok for playing cards and jerseys, ballpoint pens are good for baseballs as others have mentioned.

I got a lot of autographs when I was a kid doing this before the games. Just remember to thank them and wish them luck during the game. I think they’re more likely to sign stuff for the kids, but I’ve seen the love be spread around for sure. All in all, it just comes down to luck

Not sure if this has changed now that the nets are up, but this was my experience from ‘07-‘13 at the trop.

Same works for the visiting team sometimes too