I'm a newb on yaks, I've had one for 2 months. Initially, a yak feels really weird when you're used to a boat, and feel unstable but you soon get over that rather quickly. The 1st time I was in a yak was a sit in, and a short one at that, 10'. If I wiggled my butt the whole yak would move around, but its a good thing to do IMO as you instantly get a feel for what the yak will do. Within 5 minutes, I was comfortable with that yak and was paddling around having fun. I did not do any fishing then. I paddled around in calm water for about an hour or more and felt completely comfortable when done. We then went out into the main channel of a slow river and I was comfy there as well. I never felt like I was going to tip or turn over, never even came close to doing by accident either. Now, yes you can flip over, but you'll sense it well before it happens unless a big wave catches you by surprise. I decided then I was going to get one, and had researched on line. I went to a outdoors store and sat in a couple, liked a WS Tarpon 10 which is a sit on top. I ended up with a WS Pungo 120 (Sit in) but can rig it out for fishing as well.
Try and finds some stores that have yaks in house, and sit in 'em. You will know within 5 minutes if you're gonna like it or dis-like that particular model. After that, you need to go to some demo days, lots of shops have 'em and you can try out different models and makes. Narrow it down to a couple, and then go for it. Google can help you finds some stores with demo days,
GO BIG ORANGE !
I meant to behave, but there were just way too many other options available at the time.