If you want the best turning, you'll be firmly referenced to the toolrest. Keeping things steady there is what allows them to be round. Doesn't even have to be you holding the tool, really. 680 on squares from 5 to 15 diagonal works fine.
I use a pin chuck. Bore a 1" hole in where I want the center to be and draw the tailstock up tight. Makes for a nice stable relationship between the piece, the tool and the rest. Another non-player.
Well, I don't rest my roughing gouge on the banjo. It's too low. The rest should allow me to traverse a sufficient diadonal to reduce in diameter so I can move the whole into the space I've created underneath.
I've got three myself. The one that came with, a shorter one for stuff that's short, and a curved one for trimming inside. Don't really need the third, but it's great for tool control on a continuous peel, where I might have to move my rest a couple times.
Then listen to the voice of experience. You can't turn too slow - no motion is called carving, though. You can turn too fast, and that's dangerous. What makes you a turner is the shavings you make, and they're the same at any speed, as long as you can maintain control.