Do to the age of your linolium, I would say that it would not be safe to remove it. Do to the asbestos in it. It is very harmful. You would have to have a team of asbestos experts come in and remove that for you. Before you could even think about having a new floor installed. I usually just put a subfloor down over the old vinyl. But you want it removed and I think that you should have your floor looked at first. before doing anything with your floor.