With a 50mm lens on a DX (1.5x crop factor) body, at 20 feet/6 meters you can just barely get away with a standard 53" roll with the camera oriented vertically. There's not a lot of room to manoeuver at that distance; the paper edges are just barely outside of the frame. It is just adequate for a single full-length subject or a close couple, but with a 50mm lens, they're going to be pretty tight to the wall (3-4 feet max) for a full-length shot in that kind of space anyway. For a head shot, you then have your choice between bringing the subject closer to you or moving closer to the far wall yourself. Somewhere in the middle, you'll find a sweet spot compromise between your ability to control the lighting and versatility with framing (it's always easier to get the picture if you can move around the subject rather than having the subject move).
53" will not be enough for a horizontally-oriented camera unless you keep the subject tight to the wall and move considerably closer; you'd need to step up to the next standard size (107"). You don't actually need more than 80", but you're stuck buying what people sell, and the extra couple of feet gives you some fiddle room for framing.
If you have the room, the 107" option is probably better. The problem is that the rolls need to be stored vertically when they're not on the stand in order to avoid forming visible horizontal stripes -- the paper doesn't actually crease, but it does sort of get a "set" to the diameter at which it is bent, and horizontal storage creates two tighter-radius bends on every wrap of the core. Storing the paper vertically means that you need a 9-foot ceiling somewhere, and not everybody has them. If you want to frame your pictures horizontally and need to work in a small space, you may find a fabric backdrop to be a far more practical solution.