I haven't tried a lot of fishing kayaks, so mine is Hobie Mirage Outback. It is an expensive unit but it worth its price. Hobie is my first “good kayak”, and I'm not disappointed in this purchase. Drive system of this kayak is wonderful, it is fast and very stable. I've had no problem standing up and fishing in it. Just found this article https://improb.com/best-fishing-kayaks/, there are a lot of fishing kayaks, about 20 models.
I'd also recommend thinking about drysuit because water is cold usually. I prefer Ocean Rodeo drysuits, you can check them at their official site oceanrodeo.com. If you are not a fan of this brand, you can find more info about kayaking drysuits here.