First, full disclosure: I used to work for AndyMark.
Before the gear ratio, you want to figure out how fast your drivetrain is going. Your intake roller should have an appreciably higher speed than that, so you don’t run the risk of running over the game piece you really would rather intake. AndyMark claims 10 feet per second for a stock AM14U4, so we’ll use that for this exercise. Some people like to double it, but I’m going to go for 15 ft/sec for this.
Let’s say you’re using a 2" wheel, which has a circumference of 6.28". To get 15 ft/sec 6.28" at a time, you need about 29 revolutions per second or about 1700 RPM.
The AndyMark Redline A motor that came in your kit has a free speed of 21,000 RPM. Using a 12:1 57 Sport gearbox (or a VersaPlanetary, if that’s your jam) gets you 1750 RPM. Close enough.
By playing with the wheel diameter and sprocket or pulley sizes, you can achieve a comparable speed from other ratios as well. Hope this helps!
Edit to add: Also, make sure you’ve got something to your design so the motor won’t get stalled out. RedLine and 775pro motors die very quickly in that situation, so some combination of letting the roller slip once you have a ball, current limiting in a motor controller, or driver gentleness (the least reliable) will help you prolong its life.