I used to have a trampoline. Water can pool up on it after a rain, but it slowly soaks through. It's actually tightly woven mesh.
Liner and underlayment can be expensive, but it's worth it in the long run. It was the most expensive part of my pond, by far, but I didn't want to risk anything less given the time and money going into it. 45 mil EPDM liner is the way to go. When I first decided on upgrading my pond from 400 to 800 gallons, everyone said the one thing to not go cheap on was the liner, and they were right. I did everything as cheap as possible, except the liner.