Let's discuss all the main options, because they all have their pros and cons. Why do I mention backlighting here a lot? - Because it allows you to get the subject very close to the background without any shadows, in most setups you can even have the subject touch the background and not have a single shadow.
Paper - £50 plus stands (for a huge 2.7x11m roll
My absolute favourite. It's cheap, even for huge sizes, easy to use and looks great. Some will allow you to light from behind the paper which is a great option. Not ideal for travel, and they require some stands or wall brackets to hold them up.
Muslin/Cloth - £30
Many of them are a bit see through so be sure to check about that before buying. They crease up easily, which can have a nice effect for some things, and they are easier to travel with. Backlighting this is an option with most kinds of cloth and then creases shouldn’t show up in the image. Can be hung from almost anything without expensive stands.
Tabletop - £20 to £10
I use glass and paper for this, and it's absolutely lovely! You can also use a fabric light tent as a cheap alternative, but it won’t hold much weight at all.
Painted wall - £££?
This requires a permanent space, but it allows you to get more use out of corners and space isn’t wasted on stands to hold up the background. It's a hell of a lot more work and would usually cost a lot more too. Backlighting isn’t an option, so you would still need space between the subject and background.
Pop-up cloth - £30 to £80
These are not as large as most other options, but are very very easy to work with and great for travel. if full body shots (including feed) are not required then this is by far the best option and can be set up almost anywhere in seconds. Some of them will also allow you to light from behind the half-clear material which is great.