down to bare wood you don't actually need a primer, but a primer will make all paints stick better to the surface anyway.
I would go to Sherwin William's or a Paint Dealer and entertain this question to them. Today, latex is about as good as oil. Oil takes so long to dry that contaminates can fall on a wet area and really mess it up. Oil also takes forever to dry in winter climates. Also, remember that latex dries very fast it will not cure out and finish its trying if that night falls below 55 degrees or heavy humidity.
This might be a better Spring project than one in this season.