Yep, save your $$ and let them do the whole job. Sanding the car is a lot of work, but they also have the tools to do the job relativly quickly.
If you chose to do it, follow ProZ's advice. For protection, primer is a porous paint and is not a good cover for bare metal as it has little in the way of sealers. So you will have to paint each section after priming to seal it. In essence you will be painting the car, and then having the shop repaint it.
Check out some of the work the shop has done to make sure they do it well. Try to meet the person that is actually going to do the work. The reason? I took a car to have painted by a local 'custom' painter. His work was excellent. But he had his helper/trainee do the actual work, and I never saw such a bad paint job,...scratchs like a cheese grater, bare metal showing thru, orange peel. We made him repaint it, free or course.