building a fire pit starting with a steel ring
Galvanized gives no benefit. However.the tiny mount of zinc oxide produced would be no problem . I would suggest a local weld shop may have some stock to make you something. Material at least 1/8" ( 3 mm) thick if you want it to last awhile.  Stainless steel is pretty common, either the magnetic ( like auto exhaust) or non-magnetic. Stainless would not need to be as thick. Try a local junk yard.Bolts would be much more practical than trying to rivet. If you could find it, short length cut from large pipe like 24" diameter. Or , the old stand-by, 55 gal drum , cut off a foot of drum.