would it be better to bead blast the barrel before painting ?
You could do that carefully.
But some of those blasters are powerful, and it could break off part of a fin.
So, I'd use a lightweight media in it, and don't get too close with the gun.
Then get it real clean afterwards, inside and out, and squirt on your paint.
Alternativel, you could just clean it really good on the outside to remove all oil and dirt, and just rattle-can it with BBQ black.