Personally I'd get a heavy wire wheel for a drill or grinder and get rid of all that rust, every bit. Then I'd give it one or two coats of brush or roll on rustoleum professional from a quart can. Pick whatever color your local home depot has in stock. It'll hold up fine under there. A million times better than nothing but obviously not the best. Pretty much exactly what
@LONGJP2 just posted. The brush on rustoleum is cheap and goes on quick and thick, that's why I suggest it. No masking or over spray to worry about.