There is no universal cap sorting method.
The best cap sorting route is the one that can repeatedly separate the real closure, identify or create the required orientation, transfer it without damage and present it at the exact point the capping machine expects. A method that looks fast in isolation can still be unsuitable if caps nest, bridge, scuff, turn in the chute or arrive with insufficient control at the handover.
Start with production samples rather than a catalogue category. Diameter and height matter, but so do skirt depth, ribs, tamper bands, liners, hinges, dispensing features, centre of gravity, decorative finish and any dip tube. The downstream capper also matters: a chute-fed spindle capper, indexed pick-and-place head and rotary capper can need different presentation from the same closure.