Your going to want to start by stripping off the paint and starting fresh. Old checking and flaking lacquer you want to strip off, or even if it weren't leaving an original lacquer finish on there isn't the best plan of attack for something you plan on holding onto and spending the money that paint and supplies cost today. You don't want to refinish it with lacquer, the least durable of automotive refinishes, and due to government regulations, its not even easy to get today. Modern urethanes won't need nowhere near the amount of upkeep. They do dry dust free pretty quickly, depends on which clear and the activator, reducer used. For an overall though, you are generally best of using a slow activator or reducer or medium, not fast. This will allow more time to get around the car, the clear to lay out nice, and more time for solvents to excape, You do want to have a pretty clean area to paint with a lot of lighting, and don't forget saftey. Modern paints have isocyanates, so you want to wear eye, skin and respiratory protection. And don't forget good ventilation, and not having ignition sources where paint fumes are around.
I use a 8" orbital and either 36 or 80 grit to start stripping, but some may recommend using 36 may put some deep scratches in the metal. I get the bulk off with 36 though and once some layers of paint are removed finish with 80 making sure to sand out any 36 grit scratches in the metal. You could also go over the 80 with 180 if you don't have any bodywork to do (probably not the case) and will only need a few coats of epoxy primer, other then that, with filler primer and blocking, 80 will be fine enough. A 6 inch da could be used too, just will take a bit longer. Actually I use a combination of machine sanding, paint stripper, media blasting and hand sanding when stripping a car, they all have areas where one process works better then others. Once you have stripped the paint then you can epoxy prime and do any body work over the epoxy. What grits from there you use really depend on what you are dealing with, but I normally use filler primer over the epoxy primer and block sand with 180 and reprime. When all bodywork is done, final sand primer with the correct grit for either the paint (usually around 400-600 wet for most basecoats), or if you are sealing, sealer you are using. Get the product sheets for the primer and paint you use, cause grit information as well as a lot of other valueable information will be in them. Giving the complete process of what you should do would take forever to write, as well as being a guess not seeing knowing the exact situation with the car. But that should get you started. The bumper I believe might be urethane. I suggest you spend some time reading through the knowledge base and searching past threads, as many of this has been covered many times. If you have specific questions along the way, just ask. Many intelligent bodymen and painters on this board who should be able to answer questions you have.