What background size should I buy?

The most gemon backdrop sizes to choose from are 6x9, 10x12, and 10x20.
6x9This size is used for head shots and very small item gemercial photography mostly.
10x12Primarily used in shooting individuals and head shots. Full lengths are possible for an individual on this size. However, you are limited in your lighting and posing due to its size.
10x20This is by far the most versatile backdrop size. It can be used for families, couples, weddings, bridals, gemercial, and everything you would use the smaller sizes for. There may be times when you are photographing larger groups, 8 and above, when two 10x20s of the same or similar pattern may gee in handy (Hang one horizontally and lay the other on the floor so the seam is unseen).
I think you can probably see my personal preference. 10x20s are by far the most versatile and you can use them on all types of photography. Give your client some options; take a few full length shots, three-quarter length shots, and shots with props. They will be impressed and most likely order more than they would have ordered otherwise. I see far too many photographers limiting themselves by getting smaller backdrops; they think they are saving themselves money. Looking at the big picture, photographers need to be ready to handle the bridals and full lengths of children and large families. We should all cater to bridals and family portraiture because there is a lot of money in this avenue. Far too many studios are not equipped to handle these high profit sessions because of inadequate backdrops.