Sit on tops are plenty stable. I can stand to cast - or pee - in my Hobie Pro Angler 14" as well as troll hands free.

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The Pro Angler may be beyond your weight limit (120 pounds empty) and/or budget ($3,000) but there are plenty of paddle kayaks designed for fishing in your price range.

Kayak Angler online magazine LINK has a kayak buyer's guide every spring, and you can view that issue at the link.

Lifetime Products are made right here in Utah and they offer a dozen or so fishing kayaks, and some are on sale right now - with free shipping! LINK TWO

Finally, the suggestion of a pontoon is equally good if you fish smaller waters.

Cleverly disguised as a responsible adult.