I have a Hobie pro angler I use primarily for fishing. It's a tank when fully rigged, but it is the most stable kayak I've ever used. Stable to the point of being able to stand up to cast, turn in a circle, walk to the bow, etc. (of course now I'll probably flip it next time I go out
) They are pricey, in the $4-5k range, but it is actually one of the best investments I've made into my own leisure. It opens up a whole new world in ways that are not possible with a boat.
I've taken some gear with me on occasion if I'm going to be in an interesting area, but I would be slightly hesitant to do so in the average sit-inside kayak out of fear of sending the equipment to the bottom of the water. That's not to say you can't or shouldn't, it just depends on your comfort level.
What I would recommend, regardless of the kayak, is to have a dry bag large enough to fit all the electronics, and another dry bag that will fit the camera/lens combo by itself. The camera/lens goes into it's designated bag when I'm not actively taking pictures, and the other bag only gets opened if I need to change lenses or batteries. This minimizes the opening/closing of the large bag and the risk of potential disaster. Also, I would have the camera tethered to something other than your neck via the strap, and particularly so if you are in any type of current. Lastly, I consider a some method of anchoring an absolute must. A 3lb grapnel anchor will keep you in place under most conditions and allow you to sit and wait for the wildlife.