Do I need to prime first?
Even if you buy paint with primer I would still prime first. Stain blocking primers will keep stains, crayon marks, nicotine stains,etc from coming through. Paint with primer in it doesn't have the same ability to block stains and if you forgo that first base primer to prepare your wall for painting any stains might still come through.
Priming is essential. It is wood/gloss you are painting over. You can either ues TSP and wash walls and take chances with paint and primer combo OR go to Sherwin WIlliams and get their Extreme Bonding Primer. BEST. Only trick is you have to wait a day between paint and prime. You can tint the primer which will save coats of actual color but primer is essential. Good luck.