Looking for a good, inexpensive mini metal lathe

Hey guys,
So I've got my heart set on getting a good mini metal lathe. I have been watching videos on how-to's and whatnot, but I need to find a good one to buy, as well as the tools needed.

One I'm looking at is the 7x 10 Mini Lathe from Harbor Freight - it's only $600, but it doesn't come with any tools. I've been reading some mixed things on it, so I'd like to ask you guys. I would also consider going much smaller than 7x10 if there are any good ones, even 5" max.

I don't really need to do super complex things, the main piece I'm wanting to make would be something like this which has these specs. Most of my work would be relatively simple like that (at least I'm assuming that's not too complicated to make). That would be my starting point at least.

Another thing I'm interested in is a 4 jaw chuck, so I can drill those off-center holes. Is that something I could buy and replace on this lathe?

P.S. if you're curious as to what that metal thing I posted is, it's an e-cigarette mod, it's a new hobby I've gotten into and things like this are pretty expensive and hard to find, so I'd love to make them and start making my own prototypes and designs, but they would be relatively similar to what I posted.

TL;DR basically just looking for a relatively inexpensive mini metal lathe that can accurately make 5" (tops) and under pieces. I would consider smaller if they are available. 4 jaw chuck preferable, even if I have to buy it, and maybe some tips on tools.

Thanks guys!