I don't think there is a standard "Punk" rig really.
I think it's basically a combination of stripped down rhythmic playing and a lot of distortion. How you get that distortion is really up to you. Over the years you get all kinds of combinations and all kinds of studio tricks being involved.
They are classic combinations of hot pickups, pedals and a dimed tube amp. Tons of things like Distortion+, Rats, Tubescreamers into whatever amp was lying around were used.
I know that when I want to do a punky sound I have a few random pedal/amp/guitar combos that work better for me. Best all round punk pickups in my opinion are P90s and Tele Bridges, hot and honky. I love Blackface Fenders and Marshalls dimed pushed by a very high gain pedal, that doesn't always mean high distortion it means high gain. I can't believe how punky my D*A*M Sonic Titan is because of the volume it puts out. For traditional rock or blues I'll use a Rangemaster, but I'll use the D*A*M Sonic Titan for anything heavier like a dirty boost with the volume dimed and the distortion just audible.
I do use both reverb and delay even on punk no reason not to, just don't overdo it. I think it actually makes it sound better to have a little boing and warble on your power chords. Sounds raunchy and less cheesy then chorus and less like grunge.