JT has given you great advice.
I'd add a couple of bits of advice:
1. Not all pen kit manufacturers have the same quality standards. Some "Slimline" kits have transmissions (the bit that moves the refill in and out) that are junk, others are very well made. It can be tempting to buy a bunch of inexpensive kits from a no-name vendor, but it might be money thrown away if the mechanisms are flaky. If you intend to sell pens, stick to the reputable vendors until you are confident that you can tell the difference - because once you sell a bad pen, your reputation is on the line, that pen had better work for more than a couple of weeks.
2. Think before buying "single use" gadgets. You have a lathe, it's a simple task to make (for example) a couple of inserts to fit into the headstock and the tailstock making a very effective "pen press" (to press fit pen components into the barrels after you've turned and applied finish). And if you don't have a drill press, you can get chuck jaws that hold a pen blank, and a Jacobs chuck on a Morse Taper that fits into your tailstock. This also can have a longer travel than the quill in a drill press, which saves having to stop and reposition the blank if you can't drill all the way through in a single stroke.
3. Check out the posts that Mark Mayo posted in the last few days with video clips of how he does certain operations - cutting a blank to length, drilling a blank, gluing the brass tubes into the blank. There are many ways of doing most things, but if you are new to it simply being shown one way that works can get you started, and you can experiment and find your own way later.
4. Do not cheap out on personal protective equipment. You have one set of lungs - protect them with a quality respirator that filters out dust even below 1 micron. The 3M half-mask respirator is a good choice at around $40 (and can include filters for volatile organics, which keep out nasty things like fumes from finishes). A dust collector or an air filtration system is a good idea, but they are spendy. (Note that a Shop Vac is good at picking up chips, not the same thing as dust collection.) Protect your eyes with Z81+ safety specs or (even better) a Uvex Bionic faceshield. You can get them for $35 or less, and they will keep shrapnel from messing up your face and potentially shortening your turning career.