Well it depends on how long you are going to stay on the water, distances you are planning to cover, your ability to swim and seasons...

But lests go with basic first:
Life jacket must be of comfortable fit. Any other features are just features. I don't use mine except when in busy harbors or open ocean but I'm a good swimmer and local authorities dont care if you wear one as long as you have one. I prefer heavy duty zippers to snaps. Pockets on PFD are good for carrying extra stuff with you so if you go over you have the stuff you need.

Paddle. Spend extra money. Mine is Werner and is carbon fiber which is extremely light but very durable and I had mine for 9 years. Shaft is not round like most cheap paddles but slightly flattened giving me better grip. This is your primary tool which you will be using for long times and any wieght you can shave off counts. And in the end of the day comfortable paddle will not give you blisters.

I have a bailer made out of 1 gallon water bottle and bildge sponge which takes care of everything when I get water in my boat. Dont fall for fancy gear. There is no automatic/easy way of getting water out of your boat short of manual labor.

Basics kit: flare or signaling device, mirror, strobe and whistle
and this is where having good PFD come in: you can fit all this stuff in the pockets and have it on you. Cheap PFD dont have pockets.

Fancy stuff:
-rivers go one way so compass is less of the importance but good on the ocean,
-knife is good like Gerber Shorty (cheap and last forever),
-tow rope which I have for last 10 years and never used except for shelter building and towing my tired friends,
-kayak skirt is nice to have in the rain/white water/ocean but if doing day trips why not get a little wet but it is a life saver in cold weather
-dry bags are nice to have as well if you are doing extended trips or need a spare change of clothes but some of my friends were double bagging stuff in garbage bags and it works just as well
-small waterproof case like pelican where I put my water sensitive stuff like my car keys, phone, camera, etc etc... This is a real peace of mind especially if you just want to play wet all day and not worry about anything.
-map protective case if you buy expensive topo maps
-if you do a lot of wet stuff aka carry boat over shallow water, frequent in/outs, paddle on wet days than get some kind of wet shoe or sealskin socks


And of course basic stuff like sunscreen, hat, fak, water... ANd camping stuff if you are planning to camp.