Primer is basically a paint layer that allows the paint to stick to the object you are painting easier. It's not always necessary, but if your paint seems to run because it's too thin, then spraying on a primer coat is recommended. If you airbrush, then it's recommended that you put on a primer coat to help the paint stick to the model.
Acrylic or Enamel? That's up to you. I use to do enamels back in the day but the even well ventilated, I hated having chemicals around. I've since switched to acrylics. Clean-up is easier since it's water-based.
Glued parts? As suggested, you'll have to break it and then re-glue it. You may need to use epoxy putty to rebuild or clean up the damaged plastic.