Painting Galvanized Fence Bracket
You definitely want the primer. Latex paint has lousy adhesion on metal; it gets the nod on galvanized surfaces because oil based paints have a chemical reaction with zinc. The primary reason for the acid is to etch the surface and give the paint a mechanical bond. You really don't want to skip a primer when adhesion is such a big issue.

There are oil-based primers with a high zinc content, with zinc in the name or for galvanized metal printed loudly on the label. They offer superior performance in extreme temperatures and salt water environments. I doubt that it's worth going out of your way to find them, but it might be an option if you see one while you're in the store. You can go over them with a latex paint, just not vice-versa.

You might also be able to get them blasted for a reasonable price at a local powder coat shop or someplace similar. It really only requires a small amount of labor to glass bead something in a cabinet, but we all know shop rates can be wildly divorced from reality.