I had a New Unlined Drum also. I did Two Burn Outs in it which did Two things It helped season the inside and also took the outside paint and made it easier to Wire Brush off with my Angle Grinder and Cup wire wheel.
I then took and gave it Two coats of 1K deg Primer paint then followed that with Two coats of 900 F Header paint in my color of choice (red).
Everything Looked Great until I found out Packing Blankets and Bungee cords Melt!!!!!! It still looks good but will get touched up this Spring!!
Good Luck and Good Cookin