Whatever you do, be scrupulous about getting the old glue/foam off the backing. The backing is made of pressed dog biscuits so you'll have to be careful if you're going to reuse it. Don't be afraid to use fiberglass screening & body putty on any cracks that develop.
I used 3M headliner glue on my conventional headliner replacement job. Spray on lightly & evenly if you're using the normal headliner. If you insist on the vinyl stuff, headliner spray should be all right. Barge cement (the same stuff they use on shoes) would be stronger, but its probably overkill.
regards,
jlex.