Using the right kind of paint on your shutters is important, but I think the real question you are looking for is "How do I get the paint to stick to my shutters?".
Today the most common type of shutter is the vinyl shutter. The vinyl shutter will fade gradually over time. When it is time to rejuvenate your shutters make sure you do do a couple things:
Clean them good. Remove the oxidation with a cleaning solution like Trisodium Phosphate (TSP) and water.
Select a vinyl safe color. Use the colors that have tested not to warp due to the heat from the sun. Most paint stores can guide you to the correct color selections.
Choose a 100% Acrylic paint. Always use great products. The benifits include things such as better adhesion, better moisture protection, and mildew inhibiting features.
I don't come across too many aluminum shutters but they are still around. For these, follow the same instructions as listed above.
*Quick Tip - To paint your screws, use a piece of cardboard to hold them in place.
Back to the original question. What paint should you use? Since my preferred brand is Sherwin-Williams, I will give you the suitable products from them.
They all have there own unique properties but anyone of them will work. Call me if you have any questions @ 410-341-0605 or to setup an estimate you can scroll to the bottom of the page and book a day and time.