On the Herters choke,I can't say.They are from a time before steel shot.A conservative wild guess,Bismuth or Classic Doubles shells.Expensive!Set the choke mod or looser.
On the 20 ga:As a kid,I did not know any better so I killed a lot of Canada Geese with a 2 3/4 in 20 ga(Chicopee Falls Stevens 530 A ST)
My experience,pen raised birds will be close shots.Hopefully,you will be hunting over some fine dogs.IMO,the dogs are the real justification for planted birds.As a shooter,you are along to help give the dogs a good time.Typically,the birds will hold and the dogs will hold and you will flush the birds.They will be trying to get some altitude,They are not of the same constitution as wild birds.As the ranges are typically quite short,I do not feel a need for larger size shot.I prefer the pattern density of 7 1/2s,and likely a looser than modified choke.
If you get to go after wild birds that are spookier,flushing at longer ranges,take what you have,maybe 6's or 5's,good shells like Fiocchi Golden Pheasant.No sense shooting at unrealistic shots.Be the guy ready in the corners,bush patches above gullies,a tumbleweed by a fencepost,or tight birds that get walked past.Get the ones that take folks by surprise.your light gun is quick.
Focus on the head,not the whole bird.The rest is mostly feathers.If you shoot,watch the head.If the bird loses a bunch of feathers and rolls,watch the head.If the bird still has control of his head,shoot him again.