I'm still learning too. When I use the wheel, I pedal too fast, and the yarn gets overspun, because I'm still having trouble drafting well. When I run out of fiber, I run it back through, turning the wheel in the opposite direction to get out some of the twist.
When I use a drop spindle, the spindle swings around like crazy and doesn't spin right. I usually end up pre-drafting the fiber, spinning a little bit, then parking the spindle between my knees and pulling the spin through the fiber with my hands. It's slow, but the yarn is nicer that way.
So far, I've spun wool, silk, yak hair, and a merino/silk combination.
I still haven't tried plying, but I'll get there.