Available are plenty of different types of backgrounds, or backdrops.
You can find rolls of paper, in many different colours, and a few qualities to choose from, and you can also find different width and length.
You can find backdrops made of a fabric, printed with a motif like a brick wall, or many other sceneries.
Also are some foldable with a black colour on one side, and a white on the other. These foldable are easy to fold down, and tug away.
And available of the brand HiLite, are some other foldable being more like a box, where you actually can have your flashes inside the box for use like with a colour gel, or to make a high key white background. I have not tried these and cannot tell if they are any good. But the price tag suggests so.
What I have are two rolls of paper, one black and one white. They suit me in my current studio setup. And it is easy to cut off from the roll if the paper gets dirty. But being paper means that you can use both sides. Mine are 11 meters, so they will last for quite some time, I expect.
I did have two backgrounds made of a non -woven material. But it was a real fiasco, so I got me the paper backgrounds instead, and I am satisfied with that.
At my global-local dealer I see backgrounds in different materials, like; paper, vinyl, canvas, fabric and foldable. They also have many LastoLites with prints.
You can use a chrome key colour for the background. This can be any colour really. A green is often used because it will often not interfere with the colours of the subject, or clothing, hair, etc. Also you can find blue coloured backgrounds for the same use. Black or white can also be used, but are more likely to interfere with the subject's hair, eyes or clothing, when working on the background, in your chosen image software, cutting free the subject from the background.
A system is available, for mounting on the wall or the ceiling, with brackets that can hold up to 5 rolls of background. It is practical as you can have your backgrounds ready, but still kept away. You can find the brackets for 1, 3 or 5 rolls, and the whole system can be bought even motorized. There are expanders to be stuck inside the background-roll and will, with a system of a chain, easily be rolled down and up again. Manfrotto makes this system, and I have seen some cheaper, but similar versions.