The hobby has gone through a number of phases. Maybe 10-15 years ago the thing to do was to not only restore the car but make it far better than it was new. Cars were not merely painted they were endlessly primed/blocked/primed/blocked until flawless. Frames and undercarriage also. Striping was buried under clear coat. Brake boosters were so polished they looked gold plated. Engine bays were finished in glossy paint; bumpers show-chrome plated. The joke back then was if you brought a nice original to a show, it wouldn’t even place.
Took some time to realize that isn’t how they were built. Today those types of restorations are referred to as “prom queens” and “garage furniture.”
Today originality is King, even if there are some battle scars and rust. That stuff falls under the ‘patina’ umbrella and leaving it as-is will be admired.
As for your car:
Don’t paint anything! Carefully clean, even if it requires some disassembly. Safestrustremover can dissolve light rust without disturbing the underlying finish but you have to be careful with it.
Leave the dings, wash, and clay bar, carefully polish the paint. I hear DuPont #7 does wonders. Don’t use a buffer on it unless you really know what you are doing.
Depends on how rusty the trunk is. If it is surface rust I’d deal with that. If there is a lot of perforation, holes, etc. I would have that section replaced. The gas tank is secured to the trunk floor so it needs to be structurally sound. Rusty/damaged fuel tanks aren’t worth repairing so I would replace it. They can and do rust through.
As for the top, does it ever need to be up? They can be cleaned but by now it is probably brittle. Also, the header bow is a commonly rusted out area on converts. May be better to leave as-is.
As for the engine, make sure the builder is on-board with the originality theme. You don’t want them replacing the carb, alternator and other components with generic parts-house stuff. Make sure they know not to deck the block during the rebuild and do not let them put hardened valve seats in it. Completely unnecessary.
Let’s see the photos.
