A non-waterbased primer would be best. Zinsser Cover-Stain (oil) or B-I-N (alcohol) should be readily available at most box store and many real paint stores.

If you want a smooth finish without spraying you should follow a few steps. Prime, sand, prime again if needed, and sand again. Sometimes the substrate will really soak up the primer. You want a good blocking coat to sand smooth so two coats of primer may be needed.

After that, be careful with which paint you choose. Something like SW Duration is NOT a good choice as it uses elastomeric resins, which are too rubbery for a good finish. You want something fluid. There are some products like Insul-X Cabinet Coat (owned by Ben Moore not I believe) that are made for this application. If you need to use a more available paint, make sure it's 100% acrylic, not a vinyl/latex blend. Pure acrylics cure harder. You can modify the paint with an extended such as X-I-M Latex extender to get a more fluid application from the paint. Roll it on and immediately back brush to smooth it out. If using the correct paint and painting all surfaces laying horizontally, it should flow out nearly as smooth as a spray application.