Well,
The both have their ups and downs. For the type of fishing that I do, I'm much better off in a float tube. A kayak in the harbor is not necessary. I do a lot of surf launches like at el cap, goleta beach etc. so that's much more safe in a float tube. I have had the need to travel great distances however which would be a lot easier in a kayak. Also, much of the fishing I do is up shallow, in the surf, close to structure... And in a float tube you can easily hold your position and fish while in a kayak I would constantly need to re-position and would probably end up carrying an anchor with me or something. Float tubes are easily stored and transported and you can de-flate them if you need to. Storage of tackle and equipment is a consideration when purchasing your vessel. I wish I had thought of that when I bought my float tube. I just went for the best I could afford at the time (which wasn't much) and now I'm wishin I had saved up a little longer. Definitely go with a round boat instead of u boat. Like Pete said, they are much more stable. You'd be amazed.
When I fish Bass-N-Tubes (a float tube club) tournaments, I keep my fish in a livewell that Rob showed me how to make. It's basically made of chicken wire with a mesh drawstring top and it sits in the water next to the boat. However, when mortality isn't an issue like in the ocean, I just use one of those metal stringers with all the little clips. If I get a good fish I can put two of the clips in it and feel relatively comfortable with it staying on there. Last night my wsb did peck at my leg a couple times (I think he was mad at me) but by no means did it hurt or anything I didn't feel any pain it was just like a little tap. Didn't puncture the waders.
I can't help you out on specific models of kayaks, but anything that is stable would be choice. Expect to get constantly broad sided by wakes, swells etc. and you don't want to flip over with a rod in one hand and paddle in the other.
As far as rules go, I have never really been hassled about regulations (in this state, yellowstone is another story...). I carry a water proof whistle with me which is a good idea to have when fishing high traffic areas like the harbor because often idiots will head right toward you and then turn at the last minute just to scare you. Another option would be an air horn (that would make em turn...). I'm currently considering rigging a light pole on my float tube for night fishing at the harbor. When fishing places like the harbor just consider yourself as a by-stander or a guest and yield to all boat traffic and be courteous. We have often perceived of somebody being a jackass and ruining it for all of us and the city closing the harbor to float tubes.
I too am very afraid of losing rods. I am constantly aware of what I'm doing with my rod, how well a grip I have on it, where I'm gonna put it to land a fish or tie a knot... As long as you pay attention it will be alright (lately I've been more afraid of wsb pulling it out of my hands :D).
As soon as I have enough money (which will be a while) I'm going to get myself a pontoon boat. It's basically a cross between a float tube and a kayak. It's got two inflatable pontoons with a seat in the middle and it is equipped with oars but you also wear fins for close maneuvering and holding position. Check out the bass-n-tubes page (www.bass-n-tubes.com) to see some pics. By the way, rob did that site too. Those guys have em rigged up with storage compartments, full on livewells, castro even has a bimini top. They're no good for the ocean cause you can easily fall out and not get back in, but they are great bass rigs. Sorry for the huge post, hopefully you had a coffee break in the middle or something.
-Brian