I have all three.
If you can only have one, get yourself a good used canoe.
All the features stated here are somewhat true, but there are exceptions.
Float tubes are great for small, sheltered waters. You don't want to be using one where there are a lot of motor boats, or places where there might be dangerous things in the water, such as in salt water, or in Florida. Your legs sticking out the bottom could become somethings lunch. Currents and tides are also a problem with tubes/pontoons. And, you can't carry much gear.
Kayaks are the ultimate boat. Sit Inside Yaks are virtually unsinkable and indestructable. They can go anywhere, and float in 2" of water. They are the fastest non-powered (non-sailed) watercraft there is. And I don't get very wet in mine. No more than in any other boat. If you may have to travel through any fast water, this is a good boat to have. The only drawback is that they have limited space for a lot of gear, and it's hard to keep what gear you have accessable while your on the water. And Car-Topping isn't necesary always. If you have a truck, or van, you can do like I do, fold down or remove the rear van seats, and just throw it in the back. If it sticks out much, just tie a red piece of cloth on it, and take off. And, I have strapped both my kayak, and my canoe to the top of my Geo Tracker, using just some Wal-Mart straps and a few foam blocks. It works fine. You don't have to have an expensive Thule, unless you just want one. I've also used just plain rope to tie my boat to the car top before. I have't lost one, yet.
Canoes are great fishing boats. They are quiet, reasonably fast, and can hold a lot of gear, and have it accessable while you are on the water. With floatation bags in the front and rear, they are as unsinkable as a kayak, and much easier to get back into in the event of a spill, (but you can, of course, Eskimo roll a Yak, something impossible in a canoe). They can be carried just like a kayak. And you can find used ones for very good prices with a little patience. I would avoid the aluminum ones if possible because I had one, and it was cold, and noisy, and they tend to develop leaks in the seams with age (although it's an easy fix). But if that's all you can afford, it will get the job done. The better ones are made from polymers, and can handle some pretty serious whitewater, although not as manueverable as a yak. My canoe is a Mad River Adventure 15, and I have taken it through Class 5 rapids (accidentally), and made it intact a few times.
With both canoes and kayaks, you can cover many miles easily, something not possible in a float tube. Like I said, if I could only have one boat, it would be a 10'-15' canoe.
I wouldn't even consider a Jon Boat, or those cheezy little 'Bass' Boats that look like a truck-bed with seats. They paddle horribly, are slow, unmanueverable, and noisy. A jon boat has one redeeming quality (other than being able to put a motor on it)...they float in 3" of water.
Happy fishing.