Use Self-Priming Filler
Patches made with traditional patching materials need to be primed with a sealing-type primer before painting. Otherwise the patched areas could show through the finished paint job as foggy spots. But if you patch with a self-priming patching material, you can avoid this extra step. There are several brands; just look for the words 'self-priming' or 'with primer' on the container.
Use Setting Compound for Big Holes
It's fine to fill screw holes and other small wall dings with patching compound, but for dime-size and larger repairs, and for holes that are deep, it's best to use a joint compound that sets up by a chemical reaction. These are available in powder form with setting times ranging from five to 90 minutes.
The reaction starts when you mix in the water, and the compound hardens in the specified time. The five-minute version is nice because you can buy the powder in a convenient 5-lb. box, and the compound hardens quickly, so you can apply another coat right away. Remember, setting-type compounds are harder to sand than regular patching materials, so make sure to strike them off flush to the surface when you fill the hole. You'll find setting-type compounds wherever drywall taping supplies are sold.