There are four types of pond plants: deep-water aquatics, marginals, submerged oxygenators and free-floaters.
For your pond to remain healthy you will need a few plants from each type except free-floaters.
Marginals: These plants grow in shallow water round the edge of the pond. They not only look good their roots use up lots of minerals which would otherwise feed algae.
Examples of marginal plants include Japanese water iris (iris laevigata), the cardinal flower (lobelia cardinalis) and flowering rush (butomus umbellatus).
Deep-water: These plants grow in much deeper water and should be placed at the bottom of the pond. Waterlilies are a deep-water aquatic but they like still water, don’t plant near a fountain or waterfall.
Examples of deep-water aquatics include water hawthorn (aponogeton distachyos), arum lily (zantedeschia aethiopica) and waterlilies (nymphaea)
Oxygenators: These plants live under the water and the provide oxygen used by fish and other pond-life. Be careful which oxygenators you choose as many are invasive.
A good one is Lagarosiphon major which is evergreen and can just be dropped into the pond to root at the bottom. It will need to weeded out every so often. Another good example is the water crowfoot (ranunculus aquatilis).
Floating Plants: Free-floating plants provide shade to a pond. Some are not hardy and will die in winter, some duck down into the water for winter and reappear each spring.
An example of a tender floating plant is water hyacinth (eichhornia crassipes) and frogbit (hydrocharis morsus-ranae) will come back in the spring.