Cotton duck is the most common canvas material available. It comes in lots of different varieties; to understand these varieties, you have to understand what weight and weave refer to. The weight obviously refers to how heavy the material is, while the weave refers to how tightly the individual threads are woven together. Generally speaking, the more loosely woven the canvas is, the more expensive it will be. Cotton duck canvas is usually quite loosely woven, so it tends to be one of the cheaper options. The loose weave is easier to paint on, though it can distort a painting if it stretches too much.
Linen tends to be more expensive than cotton duck because the threads are woven together more tightly. It's therefore usually more expensive than cotton duck, though it's still quite a common option as many artists prefer more tightly woven canvases. Because the threads are woven together more tightly, linen is more durable and has a stronger surface than cotton duck. You have to pay a bit more for linen canvas, but what you get is a canvas that's stronger and more reliable than cotton duck canvas.
Synthetic fibres haven't been around for as long as cotton duck or linen canvases. As such, it's not known for certain exactly how durable and reliable they are over time. Many artists don't like using synthetic fibres because of this, but also because they're not a traditional option. Pretty much any synthetic material can be used to make canvas fibres, provided the material is strong enough to hold the paint.
Of the different forms canvas comes in, canvas rolls are the cheapest, but they can also be a lot of hard work. The canvas simply comes rolled up: your job is to cut off however much of it you want to use, then carefully mount it so it doesn't sag or stretch too much.
If you don't want to mount the canvas yourself, you should consider a canvas board. They're a bit more expensive than canvas rolls, but they come with the canvas glued on to a hard board, so you can get to work straight away without having to worry about securing the canvas.
Stretched canvas refers to canvas that has been stretched and firmly attached to a wooden frame. This is the most expensive form of canvas, though it's a very good investment considering everything's been done for you. The wooden frame can easily be hung on walls.