What sort of plants for a small Garden Pond?

The pond size is about two yards wide- One point five yards deep- 12 yards long with no oxygenator but with a couple of shelves.

 

If you're going to plant into baskets to sit on the shelves, then Houttuynia cordata 'Chameleon' is well-behaved. Iris ensata has lovely flowers. Lobelia cardinalis and Zantedeschia might need a bit of protection during the winter depending whereabouts you are in UK.
A few to avoid because they're thugs...Pontederia cordata, Typha (bullrushes), Caltha palustris, Mentha aquatica and Iris pseudocorus.
I use parrot-feather as an oxygenator but it needs controlling, as do most of them.
Go for a small to medium size water lily. The leaves block out sunlight and suppress algae.

 

Many thanks for your advice.

 

Beware of yellow flag iris. It's a lovely plant, but it just runs rampant. Mine went from being one small plant to filling my whole pond within a few years.

 

Houttuynia is wonderful if contained as @noisette47 suggested but never let it get into a border - it also invades! The pond sounds big -12 yards long! How about rheum or rodgersia or even gunnera by the water's edge?