Lovey idea! Many people already gave you very good suggestions, I will stress that regarding wildlife, it is important that you have different mini-landscapes for them to get out of the water, i.e. a little beach, and as somebody already pointed out, plants coming out of the water. This is specially important for dragonflies and damselflies.
The solar powered fountains are a great way to oxygenate the water, although I like more the kind that looks like a normal aquarium pump, with a separated solar panel. You can make a small cascade and pass a tube that will provide a natural bath for birds and other animals. I have a lot of wasps and bees coming to drink to my fountain.
Cattails could cover it, but remember they are edible! Harvest instead of weed them, is my advice. And gather some shoots of the plants you see on other ponds in the area.
Regarding lining a natural pond, traditionally ponds were sealed by adding clay, which you say you have, and compressing it. Also if you can ‘gley’, which is that kinda disgusting greenish-black mud that sits in lakes smelling badly, is very good for lining. My advice is to wait till the summer, and if the pond dries, go around your area and look for that gley mud, and cover the parts where you think it is leaking. Also shadow will be good to keep water in. Try to plant tall plants nearby that will protect the pond from the sun in the summer, and if they lose their leaves in the winter is even better.
Baytrees are beautiful but I am not sure they like water so much. I would rather plant a willow but it can get out of control. I agree that the little island is important for some animals to feel safe. I saw a couple of white wagtails nesting on the middle of a manmade cascade in a nearby town.
Try to have a nice refuge to get your own residential toad near the pond, maybe between the plants when they grow. A toad house needs to be humid and dark, so they can refresh in the hot days. You can do one with broken clay pots, or stones.