At 2 feet, you should be able to keep water lilies. They live in my pond at that depth. Quite a few things now come in "miniature" and can live in a basket of pond muck, sunk to the bottom. You need to go to a Garden center, not a pet place.
You have to be careful with some of those water plants depending on how you put them in. We used to have floating pots that worked pretty good. Some of them if planted in the water will take over with there roots and become a pain to remove.
Do you have the liner covered with rocks or sand or anything? I've never seen them damage or grow through a liner, but we used to bury them underneath pea gravel, and a year later you have quite the mess on your hands trying to remove them.
edit: I guess I should clarify on that, we didn't bury the plants, just the roots to hold them in place. Those roots can really take off and grow into everything.