Is it a vintage helmet? Old ones are smooth plastic shells that have been painted from the inside unless it's a solid color that's been molded in colored plastic. Anyhow... Of you're painting on plastic, you do want to evenly scuff the surface before the base coat. Paint + glass smooth surfaces = peeling paint. Make sure you use a primer made for plastic as well.
Now, some vintage helmets are fibreglass that has been painted. If the paint is in good condition than just scuff and spray. A nice coat of filler primer (in both instances) is always nice. Let it dry completely and wet sand it. Prep is key to a good paint job.
Now, if there are decals on the helmet, they'll obviously need removed. Not just the decal but any remaining adhesive. Remember the whole " prep is key"?
Now for the disclaimer...
If your painting a vintage lid, this doesn't matter as your helmet stopped being functional from a safety standpoint a loooong time ago. But if you're going to paint a new bucket, be aware that paint is made of chemicals. Chemicals that oft times react very poorly with plastic. Some paints (More so the solvents used to keep it liquid In the can) will ruin the integrity of the shell, rendering the helmet basically useless from a safety standpoint.
Now, get to work...