If I have a character and want something with them, I think I know what to do, I have lots of artists I watch that do just that. But what if I want logos and icons? Basically I want a logo, icon, and mascot for the site I’m making, but don’t know where to start in finding an artist to commission for them.
Logos and icons are kind of a different skill set, as you suggest. Look for graphic designers who specialize in branding. Or reach out to someone who has a nice logo and ask for referral to the artist who created it.