Do I have to paint my new galvanized steel gutters?

It is not necessary to paint to protect the gutters from the elements. Galvanize is a zinc coating. If there is a place where there is bare metal the zinc will migrate to the bare spot and coat it with zinc. As long as there is zinc on the gutter, the gutter will not rust.

Cleaning galvanized steel with vinegar is a good way to prep it for painting. I have done this for painting sheet metal panels. I believe it removes the oil that is present in galvanized.

Depends on where you live, and the amount of vegetation around. In some locations where you get plenty of rain (say Seattle) it'd be a good idea to paint the gutter (slow down the corrosion).

If you find leaves stuck in your gutter all the time, don't bother painting it. The wet leaves tend to rub off the paint in short order.

The way to get paint to stick to galvanized metal, is to wash it just before you paint, with vinegar. It is the corrosion on the galvanize that causes the paint to peel off. Vinegar neutralizes the corrosion. If you do decide to paint it, use a good mineral spirit paint.

Wipe the oil off then prime & paint

Go with the vinegar my dad taught me that years ago for galvanized steel and it works

No to paint!

If they were mine they wouldn't get painted.