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1. PFD. It's a legal requirement. Look into that. Some places also require a whistle, too.
2. If you don't leash it, you lose it. Tie everything down. You can either buy paddle leashes or paracord, heat shrink wrap (optional, but makes the knots look more neat), and carabiners to make your own.
3. If you're going to be fishing you'll definitely need an anchor. You don't want to be paddling more than you're casting. You may want to consider an anchor trolley kit. My kayak has handles on the bow and stern that I was able to loop paracord through, so I didn't have to drill any holes. Pic related as to why. If you're stationary the current might tip you over. As far as anchor specifics go I have a 10lb mushroom anchor; the completely rounded ones. I've never gotten hung up on anything like you would with a grappling style. They say the length of your anchor rope should be twice the depth of the water you're fishing, too.
That's all you should need to begin with, assuming the kayak has rod holders.
