Kayaks are plenty stable for fly fishing. I regularly site side saddle in my Hobie Revolution and don't feel tippy in it at all. I've had it out in winds up to about 25 mph (too much for fly fishing) and waves up to about 18 inches or so without a problem. If things are rougher than that I don't go out. I can't fish if it's rougher anyhow.
I think taking a kayak out into the marshes would be ok if they aren't too thick and you can find channels you can sneak through where the rushes aren't too thick.
I don't know anything about Old Town products so I'll leave that to others. I've only owned the one kayak and just used the paddles that came with it.
I would also like to make one more comment about using a guide. I think it would be well worth the cost employing a good guide at least once if you aren't knowledgeable about fishing reds. IMHO a good one will teach you more about fishing in one day than you could learn by yourself in a month of Sundays. A lot of very good fishermen use them when fishing unfamiliar waters.