I've used my Harbor Freight 7x10 minilathe (and the Cummins 7x12 that replaced it) to turn the pens. I built a simple tool rest from a piece of aluminum but should replace it with one from iron next time. Turning straight pieces using the metal turning toolpost makes for VERY straight barrels.
I use mini turning tools that I bought at Woodcraft. They work well enough, though my neighbor says they are low quality.
Here's the lathe set to turn barrel from a chunk of walnut. Well, I'd actually have a live center on the right end. This was a picture I took just to show the relative position of the tool rest.
How is the Jet Mini? Every once in a while I think about picking up a small wood turning lathe to keep the sawdust out of the minilathe parts.
Daniel