If the garage door is aluminum, then I would use an INTERIOR alkyd primer and an INTERIOR oil based paint. You want to ensure that the primer you use is a high hiding primer to cover the graffitti because otherwise you might have to apply multiple coats of primer and paint to hide the graffitti.
I suggest using an interior oil based primer because oil based products adhere better to smooth surfaces than latex primers and paints, and if that garage door was spray painted at the factory, it's got a smooth finish on it. Also, EXTERIOR alkyd primers and paints are made softer so that they can stretch and shrink with wood outdoors. Wood swells and shrinks with changes in it's moisture content resulting from seasonal changes in temperature and relative humidity. Aluminum won't stretch and shrink the way wood does, so you would have a harder and more protective paint on your garage door if you used an interior oil based paint instead of an exterior oil based paint. However, exterior oil based paints have fungicides added to them, so if mold growing on paint outdoors is a problem in your area, then you might want to either use an exterior oil based paint, or add some mildewcide to interior oil based paint. Sherwin Williams paint stores sell a mildewcide called Mildex that's meant to be added to the paint before shaking.
For the interior painting, then any general purpose latex primer would do over bare drywall. And, you could top coat with a good quality latex paint. I would opt for something a little glossier that would be easier to clean than a flat paint, like a satin finish paint. If the humidity is a problem indoors, you might want to beg, borrow or steal a dehumidifier or even an air conditioner to lower the humidity before painting and while the primer and paint are still drying.
Humidity can be a killer for latex paints because it interferes with the film formation process. Oil based paints, on the other hand, have a very robust film formation process, and as long as the substrate is dry when you're applying the paint, then weather and humidity will have little effect on an oil based primer or paint. You can basically paint a fence during a Manitoba blizzard with an oil based paint. The paint will remain wet or tacky as long as the temperatures are low, but when things warm up in spring, the paint will dry and harden just like you'd applied it under favourable painting conditions. Latex paints don't have such a robust film formation mechanism, and are easy to screw up with.