What do you wear on your feet?

It depends. It depends on where you are doing most of your paddling and the size of your boat, this often requires a compromise.
If you are mostly paddling on UK rivers then you will spend a chunk of your time on steep often muddy and slippery banks. If this is the case then footwear with a deep tread pattern to cope with the mud is a good idea. Rubber that works well on wet rock is also obviously a great idea.
If your paddling destination will be rocky and sunny with not much mud (e.g. California) then something with a less deep tread pattern but lots of rubber to maximise your contact with the rock will work well.

Other things to consider are:

• They need to attach firmly onto your feet so that they stay on should you swim.
• The soles need to be thick enough so you can move quickly over sharp rocks to rescue your mate, without doing the OO Ah dance.
• Do you want boots that will provide some ankle support/protection but might be a bit on the clumpy side and be difficult to get into your boat? Or are you less concerned about protecting your ankles but more concerned about having something flexible and therefore possibly more comfortable in your boat?
• Wetsuit boots are often the warmest option, but often have very thin soles and or soles that are very slippery, especially when it gets muddy.
• Will they fit with warm socks, wetsuit socks and or dry socks on?

Will they survive the harsh river environment and constantly being wet and then forced dried by you sticking them on the radiator or in a drying room?