After you play, take a damp paper towel, and wipe down the balls. That's all you ever have to do. No ball machines, no nothing. Keeping it simple is the best answer.
That assumes you start out with new or next to new balls. If a very worn set, maybe an application of Aramith Ball Restorer would be in order, but I've never had to do that. Damp paper towel only.
By the way, before you play in a pool room, take about four paper towels, wet them, ring them out about halfway, then wipe the table down to get that chalk dust out. That's why your balls are dirty. Then, if you're really ambitious, playing on a Gold Crown, same wet paper towels, get under, and clean the tops of the ball return rails. Other tables too. You've never done any of this, but it makes the biggest difference in the cleanliness of your balls.
All the best,
WW