Hi MotherofPearl! You'll be surprised how much water the paper will absorb, and how tough it is. As long as the Paper Weight is 140lbs (300gsm), you shouldn't have any problem.
The best way to "Womanhandle" the paper is to put a few inches of water into a bath, then put in the paper, ensuring the whole sheet is submerged, and let it soak for a couple of minutes.
Then carefully lift out the paper by 2 of its corners and let the surplus water run off. You're as well having your piece of MDF nearby, so that you can position the wet paper on the board.
At this point, you can use, as you surmise, either gummed paper strip to fix the wet paper down or, if the thickness of your MDF is sufficient, use a staple gun.
I hope the above is of some help to you, but if you want any more information, then come back to me.
Very best wishes,
PA & RSC Wigan / Warrington / St Helens