Hi. From what you have posted, at this point, I'd select the bodyshop and discuss with them what paint system they will use. You should save some money doing the priming/sanding prep yourself, but you should use a product compatable with theirs. Some color coats will specify a 'value shade' for the final coat of underlying primer, so it's possible to use a 'high build' primer under that to perfect the surface first. This is usually an epoxy product mixed per the manufacturers directions, and could be a brand different from the value shade primer used by the body shop, but it would be best to get their input first. Otherwise, later, they may blame you for flaws in the final paint topcoat that show up long after the car has left their spray booth.
Also, you'll need a good prep/cleaner to thoroughly remove hand print oil and dirt before you start sanding, or you'll work the oil into the surface where it will ultimately bleed up through the primer and mess up the color/clear coat.

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1986 560SL
2002 Toyota Camry
1993 Lexus