The width of a kayak is an important factor in stability and speed. The wider a boat is the more stable it will be when getting into it, paddling, and getting out of. Wider boats have two main drawbacks: speed (or lack thereof), and the increased effort required paddling it. The wider the boat, the more surface area is in contact with the water thus making it slower.
Wide kayaks, because of their stability, tend to follow the surface of the water. In calm water when you tilt, the kayak doesn't tilt much. This advantage in calmer conditions can be a disadvantage in long trips over rough water, as the kayak reacts to the ever changing slope of the wave tossed open ocean. A more "tippy" kayak ignores most of the motions of the passing waves.
Plastic is heavier, more resistant to damage, harder to repair. Fiberglass is lighter, easier to repair, results in finer lines, but is more expensive. Fiberglass is generally more rigid than plastic, which can result in a faster boat.
Wood is light, easy to repair, needs maintenance. There are also a few companies that manufacture wood/epoxy-construction kayaks, but they tend to be more expensive.
More exotic materials (like Kevlar, carbon fiber) tend to be lighter and costlier.
You can pad any boat, but it should fit fairly well to begin with. The contact points with the boat are the feet, knees (on the underside of the deck), hips (on the sides of the seat), and bum (on the seat). The size of your feet is a consideration too. In general, a sea kayak needs to be comfortable because you are going to be in it all day, perhaps without a break. Some people prefer a looser fit in a sea kayak than in a whitewater boat, allowing space to stretch and move about.