I bought a thermoformed rather than roto molded kayak for my girlfriend. It is MUCH lighter than mine, and stable enough to stand in, although I rarely do...about the same dimensions as you. It was a Jackson Kilroy LT...but Jackson got out of the thermoformed boats. Supposedly they're not as forgiving to being dragged or direct hard hits on hard surfaces.

That being said, I never drag my kayaks ANYWHERE. A cart makes things so much easier, and keeps your boat's hull unscratched.

Eddyline makes thermoformed boats, and some geared towards fishing: https://eddyline.com/kayaks/fishing-kayaks

I'd definitely lean towards a 12 foot, if not 14 with our dimensions. Mine are both about 13.5, and although they hang out the back of the pickup bed, are easy to put in and out. Those putting kayaks ATOP a vehicle might shop for the lightest possible. A dedicated kayak trailer would allow just about anything.

If you fish cold weather, a sit inside offers more protection from the elements, yet, if swamped, is much more difficult to perform re-entry. They are also quite stable as your center of gravity is at the waterline, if not slightly beneath. They have a lot of space inside I find for most models.

A sit on top there is no worry about water coming overboard, as it drains right through the scupper holes. Reentry is I find quite easy, and should be practiced each season. Center of gravity is a bit higher sitting on top, and some models even offer seat adjustment height. Yet depending on width, most are amazingly stable as well. Storage is often limited to a hatch either up front, behind you, or between your legs. I find it much easier to find and access stuff in a jiffy in the sit inside, but it is protected from the elements and safe in the event of capsize with a sit on top.

A consideration for either...wider kayaks are more stable, yet give up speed and the "glide". The narrower you go speed increases, but you sacrifice that stability. Longer kayaks tend to have more glide, and more weight capacity.

I have one of each style. I like both for different reasons. When I got my first kayak, I felt as though it was tippy, but that feeling vanishes as you become more familiar with your boat. I never give it a second thought now. I fish on Saginaw Bay and Lake Huron with mine, so we're not talking small waters, but more like inland oceans. Watch the weather like a hawk, and use common sense, and most importantly a life preserver. Never tipped by accident yet.