At Trek we used a hot phosphoric acid bath on bare frames. Phosphoric acid was particularly suited for that purpose as it dissolves rust much more rapidly than it does the base metal and it simultaneously etched the surface to provide an ideal bonding surface for paint. A hot phosphoric acid bath might not be practical in your home, but consumer products such as "Naval Jelly" also contain phosphoric acid as the active ingredient and may suit your needs.

N.B. I had this bare steel fixture dipped in the phosphoric acid bath at Trek about 25 years ago, and it's lived in my damp basement ever since. It's held up pretty well: