I wouldn't use an MDF product due to the fact that it's not moisture or mildew resistant. In a bathroom situation, you will need those features. A hardwood product that is moisture resistant or fiberglass would be the way to go. Also, as well as MDF, they all come in 1/8" thickness. I don't see why you would need anything thicker and would be easier to work with. And cheaper if using hardwood. The fiberglass would probably be double the price per 4 X 8 sheet, but would be your best bet in the long run. Can be worked the same as the hardwood. Very easy to clean and no moisture damage worries. Available in colors and any of the big box stores.
As far as cosmetics...
Liquid Nails would probably work well in exposed areas. As long as the surfaces in contact with the adhesive are intact and clean enough. I would also brad the perimeter edges (hidden with moulding), around the vent (hidden with vent bezel), and under the ceiling light fixture.
And as mylo mentioned, I hope the roof leak is repaired. Otherwise, you will definitely have more work ahead of you.