You do have quite a few choices. Elodea is a good pond plant and it has dual benefits in that it creates shelter, the fish will eat it, it self roots and I personally like the look of it. It will grow without potting and the simple trick to sink it is to put some rubber bands around the bottom and slip a pebble under the rubber band to sink it. Foxtail is another good under story plant and loves shade and has a softer look to the foliage. Milfoil comes in about 4 different varieties and is a very good oxygenating plant and likes to be in shallower water. Valesenaria comes in a few varieties as well and goes to the bottom of the pond. Val, Elodea and milfoil are all good oxygenating plants.
For the surface there are also a number of plants you can use such as Hysop, rotola and many others. These plants like to be a water level or just below water lever. You can either buy float rings that the pots slip into and the plants float around the pond and stop the fish eating the main plant. I personally use one of these for my hysop and it has now grown to about a third of the size of my pond.
You could make your own using polystyrene because once the plant grows you wont see the ring anyway.
For height out of the pond you could use rushes which vary from 400mm - 2.5metres tall. You could also use lizard tongue or pickerell rush (excellent filtration plant)
I also run Mashwort which has a similar leaf to water lilies but the advantage it has is that it does not become dormant so therefore you still get surface coverage.
I also use duckweed because it has multi functions. It acts as a sunblock, absorbs nitrates (Helps prevent algea and green water issues) and the fish love to eat it. The disadvantage it can take over but simply net it off and use it as compost. It is a great fertilser.
I have a few of these plants in my pond and I run all my ponds biologically. My water is crystal clear.
The only disadvantage running a pond biologically is that you do loose a fair bit of visibility because you need to aim up to 70% plus coverage of the water surface for it to work effectively.
Not sure what state you are in but I could and would be happy to give you some cuttings.(if interstate you cover the postage) Otherwise let me know and I can put you onto a person who does grow these plants and does send interstate. Hope this helps and feel free to pm me if I can help you out.