I use a small awl from Lowe’s to pick mine out. Much easier on the hands and the perfect shape. I’ve traveled the world with my stud kit and it has a magnetic dish, a safety tap, my awl, a draft horse shoe nail, a wrench, and WD40 in it. I don’t have a preference on plugs (or even use them all the time) and even just use some cotton wool from the vet kit.
My studs are just cleaned with water and towel and then dried and sprayed with WD40.
I also have the tap piece that the farriers use on their drill - used it more than once to fix threads. It’s been passed around the trailer park at many an event. I just use it with a wrench.
I keep it all in an old school square lunch box and my studs are in these little Dewalt organizers. Recently upgraded to two of those instead of just one for more organization. You really don’t need a lot - I’ve run many events with 7-9 horses and just my one tray of studs.
Studs wise, you can easily get away with a set for good, wet, and hard ground. I almost always use the same studs in both the inside and the outside.
From this link, this is what I would recommend:
Good-
Front: H
Hind: D
Wet-
Front: A
Hind: B or Q
Hard-
Front: R
Hind: S