What you need depends on what you are doing. Sounds obvious really. Here are my (Ian Morris) thoughts.
Starting out in the pool
Minimum is what you would need for going swimming in the pool, i.e. swimming costume/trunks, towel and money for the pool session charge. Also it is expected that beginners can swim. The club has the necessary equipment for beginners to use at the pool - kayak and paddle and, not equipment, but the necessary instructor to tell you what to do to learn what you need to get better. Spraydecks (the thing goes around you to stops water getting in the kayak) are available and you would soon want to be able to use one. Bouyancy aids are also available but are not essential in a pool.
Staring out at the Queens Dock or Crosby Lakeside
It's cold outside - always - compared to a pool. So typically starting out you want to wear stuff that will keep water splash off you and keep you warm. I started out with swimmers, normal tee-shirt (horribly cold and wet for while when you fall in), jumper, trousers, old trainers and then somewhat waterproof cagoule top I'd go hill walking in. Also I had waterproof trousers like the cagoule top mostly to avoid the wind chill when you get out of the boat onto land. If you have a wet-suit its better to use this but you still want a jumper and cagoule top to keep warm and dry. If you have water shoes you'd got for summer holidays on the beach, or wet-suit socks, or wet boots, so much the better. The club has bouyancy aids - essential equipment outside for you to use. Also spraydeck, paddles, kayaks and canoes the club has available for use. If you are doing any canoe polo, club helmets with faceguards will be provided. As with pool sessions, an instructor will be present to guide you. As a beginner there's no going on the water until the instuctor says so.
On or near the water:
1. Do as the instructor tells you right away.
2. Do as the instructor tells you right away. If you don't know why, ask after you have done what you have been told to do.
I'm sure there is more that could be said but the instructor and fellow paddlers will all be aiming to keep beginners safe and progressing in learing whether you notice or not.