Yes, you can make a spindle from old CDs, a piece of a dowel, and a cup hook. You also need a grommet to reduce the size of the hole in the CD to make it fit on the dowel.
Another option is a piece of dowel, a wooden toy wheel from a hobby shop, and a cup hook.
Yet another option is a large bead mounted on a wooden skewer. This would be a support spindle, rather than a drop spindle so sharpen both ends of the skewer. You will also need a small bowl to support the spindle. With this type of spindle, you spin off the point so no hook is needed.
Dog combs work very nicely for combing wool. Small batts of wool may be cared by using 2 slicker brushes.
It's quite easy to make the equipment needed to start spinning.
But fair warning - it can become addictive very rapidly
