To keep the paper flat I use old, out of favour, coasters. I line the (few) open shelves as well - those that stuff is displayed on rather than in constant use, and I put an old placemat on the shelf as well. It looks marginally better than lining paper, they are easily cleaned, and they are easily disposed of when they become uncleanable.
I smled to myself when I unearthed this...
.. I guess it must be getting on for 33/34 years old now. I loved that picture back then. It was very popular, and I think I probably had that as a picture on a wall in my first house. The mat is in susprisingly good condition.
That snail one was from a set of 4, I had to buy 2 sets to have enough. I don't know what happened to the others. These were also from my first house, and I think it was when I started to have my own identity. These didn't get replaced because they were grotty, I think we moved house and I bought some new ones.
I suspect that I was a bit more careful of my placemats back then, or I didn't use them much (we ate out a lot), or maybe I just changed them frequently. It took me many years to paint the new kitchen in this house, I just had an expanding number of tester pot swipes on the walls.
I've lost count of the sets of placemats I've had and ruined.
My current table mats have been in use for... I don't know. I've been semi retired for 12 years, and the mats were well established then. I looked at them with a fond sadness today, as I realised that they are all peeling, or stained, or damaged.
They are by Rob Scotton, and they've been really really well used. I don't think you can see the damage too well in the pic.
I'm going to retire them, and get some cheapy ones to replace them.