@Kymberly You can use regular knitting wool, even loosely spun, as weft. I weave with knitting wool all the time (my local yarn store caters more to knitters). For weft almost anything goes.
You can use it as warp too, just try to pick yarn with more twist that doesn't immediately pull apart when you tug on a sample. I have even used a local worsted, almost homespun, wool as warp, I just made sure it was under less tension.
@Kymberly I should add that there are exceptions. Some projects (weft-faced projects and rugs in particular) call for very high warp tension. In that case you are better off using rug warp which was designed specifically for that purpose and has high tensile strength.