Re-installing new sheet metal. What size hole for the plug welds? Not concerned with "factory appearing", most will be ground flush and get a coat of filler if necessary.

Depends on where it is. This an old Mopar I presume? The old cars have much larger spot welds than modern cars do. In some areas (rocker panels) they are downright massive. Measure a factory spot weld and make your plug approx. the same size.

3/8s or 5/16s works fine.

5/16" is the auto body standard for sheet metal plug welds.
3/8" will work but will require more welding and grinding.

DO NOT use the cheap 1/4"hole punches for sale everywhere. you can't get proper penetration all the way around the punch hole on the base metal.

Why is that ... because the holes are too small ??

I have a couple of the cheap china hole punch tools and they are not even 1/4" I would guess it punches a 3/16" hole which is way too small for plug welding. I usually use the punch then come back and open the holes up with a step bit. I have found 1/4" is good for most where your welding sheet metal to sheet metal. If your attaching to structural pieces (frame rails, shock tower, etc.) you want a larger hole. If your using a mig set your heat up higher than usual and dial the wire speed back a hair. Angle your torch so the wire hits the center of the base panel 90° and then fill the plug from the center out.
Another thing to note is you will find that many of the factory spots either have poor penetration or are simply not doing anything at all. This is usually caused by small gaps between the panels when welding. Its very important to have the panels pulled up tight together and both panels clean on both sides.

yes. the hole is to small to get the wire in the hole all the way around the circumference of it before the weld puddle fills it up.
if you did destruction tests of your welds you will see improper penetration.

I agree with much of what is said above.
I've used a smaller hole in areas where metal was thinner. Best thing to do is take two scrap pieces and mock up what you want to do.
After a mock up of a couple different size holes and techniques now try to disassemble it. You'll find which methods and sizes work well.
Even smaller holes in thin metal are often much stronger than the metal itself...
More frequent spot welds will also increase strength.

In a few areas I have used a mig with the heat way up and used no hole and gotten great results...problem with that is a little too much time spent in any given area is a big hole thru 2 layers... The opposite side of the panel on this type of weld will produce a good match for a factory spot weld...

i typically use 5/16, 11/32, and 3/8" depending on the material sheet thickness. on 1/8-1/4" chassis plugs, i usually go 3/8, 7/16, 1/2" depending on the item in question and number of plugs used.