Trying to keep it simple:
You will want to figure out whether it is a lathe, router with rotary axis or mill with rotary axis. All three are capable (with appropriate programming) of making pen bodies. The router and mill (with rotary axis) will be capable of embellishing pen bodies (engraving names / artwork, caving (e.g. fluting)).
How do you tell them apart?
The lathe will use a non-rotating tool (like a scraper) and will have two axes of motion computer controlled (movement perpendicular to the work and movement parallel to the axis of rotation). The rotation of the work is not controlled by the computer and is driven like a standard lathe.
CNC routers and mills share a lot in common, but a mill is a much beefier piece of equipment that is typically designed to handle the stresses of cutting metal. CNC routers are not intended to do any serious work in metal (unless they have been modified with higher power spindles with wider speed range, stronger linear motion components and framing). Usually a router has a fixed table with the spindle on a gantry that moves in 3 (or more) directions. A mill has a spindle that is fixed laterally, with a table that moves in two directions. Both the CNC router and mill can have a rotary axis attached to them for rotary work. This might look lathe like, but it might not.
In my opinion, a cnc lathe will be the least useful for pen making. An experienced pen turner can easily beat a CNC lathe for production of pen bodies when you consider setup and finishing time. Component quality at par, a cnc mill is probably a bit more versatile for pen making than a cnc router if you have any desire to work metal. A router will typically be capable of faster production on wood / plastics.
The major hardware components are linear motion components, motors, drivers, power supply and controller. For software you will need something to do designs (3D will give the most flexibility, but a lot can be done with 2D) as well as something that will convert your design into the code to run the lathe/router/mill.
For a router / mill you will want to insure that it will accept 1/8" & 1/4" shank cutters at a minimum. You don't need the ability to accept anything smaller for pens and anything larger would be overkill for pens.
If what you are looking at isn't a turn-key system with everything included and working, you will have to decide how much money / effort you are willing to invest in learning how to make a partial solution work for you (big numbers can apply here). The availability of online forums dedicated to whatever it is you are going to look at will be a big plus.
For what it's worth.......
Ed