As ever, this avenue of the sport depends a lot on where and when you are going to go Kayak fishing.
In the hot summer on a calm day you could just wear your shorts and t shirt but remember when you are at sea and maybe a few hours from the beach you can get caught out, and on the sea is not the place to be found wanting.
Your safety has to be the most important thing in the world and the correct clothing is one of the most important choices regarding this.
I always wear a PFD (life jacket) but I will cover these in another post. But I also always wear a wet suite. In the summer I choose a thin summer shorty suite. They offer you a bit of buoyancy and a lot of protection from the breeze should it start to rough up a bit. The thinner summer suites are easy to paddle in and worth buying.
I also have in reach a CAG. This is a windproof over the head jacket. Its not a dry suite, just a jacket. This device over a summer suite will keep you warm in quite cold conditions. I grant you that in the summer you will not need it when the sun is hot, but as afternoon comes and the on shore breeze picks up you may well get cold really quickly.
For the winter I have a full length thick wet suite, over this I wear my CAG, than my PFD over all of this with wet suite boots and gloves and sometimes a balaclava. I fish in Cornwall so its never really bitter so I have managed so far without needing a Dry suite, but as I get older I may well move over to a full dry suite.
Rash vest can be worn under your wet suite to prevent rawness to the skin, but they also add another layer of valuable warmth. The key to staying warm is LAYERS.
Most of the time I wear mesh trainers on my feet to protect me if I land near rocks or an unknown beach. These are replaced as mentioned above by wet suite boots in the winter. The other consideration is getting sunburnt feet in the summer. Its really painful and you are knocked on your ass for a few days!! I have suffered from this.