What do I need to record about catchers?

Record the innings each player catches, because catching affects who can pitch and pitching affects who can catch:

• A player who catches in four or more innings can't pitch that calendar day.
• A pitcher who throws 41 or more pitches can't catch for the rest of the day.
• A player who catches three innings or fewer, then throws 21 or more pitches, can't catch again that day. If they reach 20 while facing a batter, they may finish that batter and keep their catching eligibility.

Note the pitch count at the start of each batter too. League pitch count reports, such as GameChanger's, include innings caught and the first-pitch number to the last batter for exactly this reason.