If you apply paint directly over new drywall, you will end up with poor coverage in certain areas. To generate a uniform finish, apply a base primer. If you choose to purchase a Kilz brand primer, opt for one with stain-blocking abilities, or you may end up having to apply several coats of paint to generate adequate coverage.
New Drywall
When drywall is first installed, drywall mud is applied to the seams to fill gaps and promote a smooth transition from one piece to the next. Unfortunately, this mud tends to absorb paint at a different rate from the rest of the porous drywall. This can cause what's known as "flashing," where the drywall mud appears lighter or duller than the rest of the wall. The right base primer will help prevent this occurrence, but only if it's applied in the proper manner.
Kilz Primer
Kilz stain-blocking primer is well-suited for new drywall and encourages a uniform finish. Available in both water-based latex and oil-based varieties, this particular type of primer is fast-drying and works as a sealer and primer. Kilz oil-based primer tends to block stains better than latex; however, since you're not blocking stains, you may want to opt for the water-based latex, because it is less toxic and easier to work with.
Application
Before applying Kilz stain-blocking primer to the entire wall, spot-prime the drywall mud to ensure adequate coverage. Prime only the drywall mud, using a paintbrush. Wait two hours before applying primer to the entire wall — including the mud — using a roller. Don't forget to spot-prime the drywall mud that runs along the seams, or these areas may flash through the painted finish.
Considerations
When applying primer, be sure to use the appropriate paintbrush. Synthetic polyester-bristle brushes are suited for use with water-based latex Kilz primer; however, they will not work with oil-based varieties. If you choose to use Kilz oil-based primer, use a paintbrush equipped with natural bristles.