I hear Kayak's are just empty calories, so I'm assuming you'll just catch and release.
Can you run a trolling motor on a kayak?
I kayak fish on the Devils river just south of Loma Alta. It's a blast, pack light, bring along a lightweight rig (maybe 8-10 lb test) and a soft case full of ground bouncing artificial baits. The beer situation is fixed by getting a soft ice chest and securing it with the bungees on the back of the kayak or by putting it in your lap, most soft chests can hold a 12 pack very well, for empty's just crush them and throw them in your leg space. If you want to catch and keep, just run a stringer off your belt into the water.
The main problem though lies in getting back in your kayak if you for some reason decided to get out of it in deep water. I'll let you figure that one out yourself.