I would try sanding to smooth out the texture and you may have to use a vibrating sander to smooth it out. Then prime it with an acrylic bonding primer such as Zinnser 123 or Aqualock and finish paint it with a flat latex wall paint which will show up any texture left less than a paint that has a sheen such as eggshell.

Be sure to wear a dust mask when sanding.

If the texture is too hard to sand out smooth, it is easier to skim coat over the walls with drywall mud and sand that. The walls will become perfectly smooth. Beware of the dust from sanding. Curtain off the area with plastic, wear a dust mask and turn off the air conditioner or heater to avoid the dust from going into your ducting. Another sanding option is to wet sand. You can buy sanding sponges at any paint dept. and use a bucket of water to keep the sponge wet. This will eliminate the dust problem.

After that you're ready to prime and paint.