Yes, you can sand back to the primer everywhere, but I wouldn't make that the goal.
The goal is to provide a smooth (but not too smooth!), level surface that the new paint can adhere to (and of course that adheres to the metal). In some places, that might require sanding back to the existing primer, or even bare metal if you need to do body work.
Be sure to scuff the entire surface, but all you need to remove is the oxidized or damaged paint. The damage will probably be worst on the horizontal surfaces (hood/bonnet, roof, trunk/boot) and not so severe on the vertical surfaces. If the existing paint is sticking well, so will a topcoat.
If you find you've made it down to bare metal, a basic spray-can primer will keep rust from forming. Epoxy primers (two parts need to be mixed) are more durable, but are not as convenient. Although you don't have to have a spray rig -- you can brush on epoxy primers, take care not to apply too thick a coat, plus you'll have more sanding to do once it hardens.
Don't make the surface glassy-smooth. On the first car I restored, I made the mistake of sanding the primer down to 600 grit or higher, which was not only a lot of work, it was too smooth for best adhesion. Gloss comes later, from the paint or the clearcoat. I stop at 220 grit (or maybe 320 at the most if it's a very thin paint).
If you're going to do this over time, when you finally think you're done, give the body a super good wash, rinse and dry with clean cloths. You might find that you need to touch up areas that have gotten dirty, damaged or oxidized since you started. Then just before painting (e.g., just outside the booth), give it a cleaning with solvent to remove any remaining traces of grease or oil, and don't touch it after that! (Your hands are oily.)
Also, if you're not going to spray it yourself, talk to the body shop who will be. If they're not completely indifferent, they'll let you know what they want. (Also, talk to several shops and ask to see some of their recent results. They vary a lot in level of care.) If it's a cheap place, sanding it yourself will mainly just get you a better job. Removing all the lights, trim and seals yourself will probably also help with the quality and cost. For the best job, you'd remove the windows as well, but you can get passable results with careful masking.
Another way to get a better paint job is to use a really good quality paint (which unfortunately isn't cheap). I like urethanes over acrylic lacquers for longevity. If you were spraying it yourself for the first time, I'd recommend a single stage urethane (one paint provides both color and gloss), but any shop should be competent to do a two stage (color coat plus separate glossy clearcoat).
I don't have particular references/research for this -- it's all based on doing it wrong myself and learning from that.