Except with tiny pieces, I nearly always start with an under-painting. Although I don't use a lot of ready- painted paper, other than those with dyes, most of my work incorporates acrylic paint as an important ingredient, both beneath the collage material and on top of it. Please note that oil paint should never be covered with water-based media.
I usually start randomly, and when I don't, I often regret it. My purpose is twofold. Firstly, random marks are more likely to allow for 'happy accidents' and create unexpected interest. Secondly, for me it is best to work from the unknown to the known. My whole creative process relies on reacting to what is there, adjusting, and then reacting again. So getting that 'white canvas' covered is an essential preliminary.
Large work can benefit from the contrast between textured collage and thinly painted canvas, sometimes textured first with gesso. Indeed many is the piece that I have spoilt by covering over too much of the original painted canvas. There is something about the way paint sits on canvas which is intrinsically different from collage material.
Collage can be enlivened and unified with paint applied on top as well, or half-hidden within the layers. I like to provide a wide range of marks, varying from the thin graphic lines of paint sticks and markers, to thick juicy brush strokes and splatters, drips and arching sprays.
I used to use oil paint quite often, at a time when I made more frugal use of the collage materials, and, providing oil paint is only used on the top surface it is fine, but, once on, it does prevent the further use of other materials, which is why I rarely use it these days.
My feeling is that whereas with acrylic it is fine to balance the use of collage and paint fairly evenly, with oil it is best to allow one or the other to dominate. Maybe I need to return to using it more often, and experiment.