I do like my little HF mini lathe, but may convert it to the 7x14 size by buying the longer bed, and a nice 4 jaw chuck would work really well on it too. I've heard you can put up to a 5" chuck on these and there are several improved type tool holders avaqilable out there... the tool holder it comes with is as close to useless as it comes, but will get you by when just starting out.
What I do when I use that tool holder is put a cutter on one side and secure it, then put a 5/16" piece of bar stock on the opposite side of the holder to increase rigidity then I set the gibs a little more on the tight side since the compound rest can move quite a bit. It can cut really accurately as long as I don't try to cut too deep in one pass, do the work as close to the chuck as possible and use the live center to help stabilize the work. A steady rest would be a really good investment for these little machines too since it'll prevent the work from flexing in the middle.