Turn between centers and do away with the mandrel. As for drill bits it is best to buy them as you need them for whatever kits you are ordering. Staples would be 7mm, 10mm, and 27/64" for starters but it really depends on what kits you want to make. Get thin and Medium CA to start with. A set of Micro mesh pads and 220 through 600 grit sand paper for finishing is a good start too.
Ok .... you're giving this advice to a beginner, here.
Someone who's never made a pen before is going to have a lot of difficulty getting going without mandrels and bushings ... After someone's been at it for a while and become accomplished at the basics, THEN propose turning between centers.
As for the advice about not using "kits" ... well, it depends on the type of kit and what's in it, really! If you need the majority of what's in the kit and it would save you money (say, the mandrel saver starter kit, where you get a mandrel, the mandrel saver, a 7mm drill bit, and 5 7mm bushings) and you happen to want or need ALL of that, then yes, it's a good idea to get that kit. Make sure that whenever you buy any tooling (like the mandrel and mandrel saver) that you always double check to ensure you are getting something that will match your lathe. In your case, I'm assuming you'll need a #2 Morse Taper kit. I use a mini lathe from Harbor Freight, so I use the #1 Morse Taper kit. They are NOT interchangeable.
Furthermore, for kits ... if you are getting a "starter kit" for a type of pen and you have none of the accessories that you'll want to get going with it ... yes, that's a great idea! For instance, PSI often offers a deal with some of their higher end pens that helps get new turners in the door. "Buy 1 Jr Majestic Rollerball in "XXXX/YYYY finish" and we'll toss in a set of trimming sleeves, 2 drill bits, and the bushing set that matches!"
Lastly, in the case of kit pens vs kitless .... you do NOT want to attempt a kitless pen without a LOT of experience under your belt. Kitless pens are generally made with a MINIMUM of store-bought parts. If you can't machine all the parts of the pen yourself, you're stuck! Stick with using a kit till you feel you are ready to take the plunge .... and then start out with small modifications, like removing/swapping components, changing the style of a finial or cap, or adapting one kit's parts to fit another kit to compliment the style.
As for what I would grab, if I were in your shoes right now .....
Starting with a mandrel saver package:
https://www.pennstateind.com/store/PKMS2SET.html
This package gets you the 7mm drill bit and 5 7mm bushings for spacers, the mandrel, and the mandrel saver in #2MT
and getting a basic 7mm pen package:
https://www.pennstateind.com/store/PKSP105A.html
This package gets you 3 sets of bushings and 2 each of 4 different pen styles. (bushings for standard slimline are the basic 7mm bushings that came with your mandrel) You get slimline, trimline, designer, and comfort grip styles. Each will have one 24kt gold finish and one other, usually satin chrome, but I believe the trimline alternate for me was a gunmetal color. This package also includes 10 cocobolo blanks, which are a gorgeous wood. Make sure you use a dust collector, as cocobolo oils and dust can be a bad irritant ... many people have adverse reactions to it.
for trimming your blank and squaring it:
https://www.pennstateind.com/store/barrel-trimming-system.html Pick something reasonable from this selection. If you have a disc sander with a miter slot, then you may want the universal pen blank squaring jig. (will be one of my next purchases, but I'll have to put my sander back together, lol) If you dont have or want the sander, then you can try the barrel trimming options. Just stay away from the carbide one! I hear it's much too aggressive and will rip blanks apart on you.
You already have a chuck, pen drilling jaws, and a drill chuck, so that's everything you need already, including your chisels.
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