I have about 25 autographed balls from mostly HOFers. When the collection was smaller I would pair each ball with a card, put them in a holder such as these (https://www.amazon.com/MLB-Ball-and-Card-Holder/dp/B000LOKJN8), and then place them on a shelf.
Nowadays, I have two custom-madewooden cabinets that can hold alternating rows of balls and cards. I have a card of that player matched with each ball. The cabinet has lockable uv-protected glass doors, but I also keep it out of direct sunlight.
By the way, if you are looking for many of the ball and card holders, I can ship them out for a nominal fee+shipping.
--Jesse
Set collector focused on completing sets and collecting Andre Dawson, Mark Grace, Greg Maddux and Ryne Sandberg.