Any of them are going to work fine for a home studio, presuming you have the space to set things up. Some things to consider, however, are:
Stands to hold the backdrop. It may seem a little obvious, but if you want to have flexibility in your use of backdrops, at least a basic stand is going to be something to get.
Reuse of the backdrop(s). Fancier ones, with special designs and images, are probably going to get less reuse for non-professional work unless you want all your portraits to have much the same look and feel. Basic ones, in colours such as black, white, etc. are probably going to see a lot of usage because they are flexible.
Paper has the advantage of being low cost and, in some ways, low maintenance, but eventually you run out and have to replace it, but being paper you can actually do a lot of stuff to it (like paint it, draw on it, etc.). Fabric, on the other hand, has to be cleaned and maintained, but is going to last, and you can adjust the drap to create depth or additional texture. Either option, by the way, will allow for people to stand on it, it's the length that matters there.
Your space. Background widths vary, so do you have room for 8' or 5' or more or less? No point in getting a backdrop you can't fit in the space. Same goes for ceiling height, you don't want the stand top in the shot.
Lighting. If you're working with a basic one light setup, you may end up not even seeing the background in the result! Especially true of on camera flash, which is the worst option for this kind of shooting. So, do you have the means to light the subject and the background? It's a consideration, I wouldn't invest a lot in a background I won't even see in the shot.
Do you want to do chromakey (green/blue screen) so you can do background replacement? Cloth may be the best way to go there.
There are probably a ton more considerations, but I think answering many of these will help you pick better options. Bear in mind, it's not as if you're stuck with paper or cloth, you can do both and both have their places.
DIY is possible, to some degree, mostly around the stands and basic lighting. For fabric or paper, you're buying unless you have your own paper or textile mill. Now, you can get fabric from a lot of places, but large wide panels are much harder to find at consumer oriented fabric shops (I know, I've tried). You can sew panels together, but doing that seamlessly would be a serious challenge. All in all, in my own attempts, I just came to the conclusion that it's a lot less effort to just get it from a photography store.