I know this has probably been done to death but I would still be grateful for suggestions as to paint and prep on a garage door. White eggshell will be the finish I am going for.
Bedec Barn Paint would be an excellent choice but would be a semi gloss or satin, you need to tackle the rust first so a good clean down and neutralise the rust with a rust killer/inhibitor, When dry patch prime over the treated areas with BIN along the other areas of concern (as shown in photos). Another paint to consider would be Zinsser AllCoat Exterior Satin available in waterbase and a solvent base.
I did my garage doors with Bedec satin on Astra's recommendation three years ago. Still looking great.