Should I measure over padding?

Yes. Always measure over the arming garment or padding you intend to wear beneath the armour, so the finished piece fits in use rather than on bare skin.

How do I size a helmet?

Measure the circumference of your head just above the eyebrows and around the widest point at the back; that figure, plus room for a padded liner, sets the helm size.

Margrex

How to Measure for Armour — A Simple At-Home Fitting Guide

You don't need a tailor. A soft tape, a friend and ten minutes give you accurate measurements for a mail shirt or helmet that actually fits.