ooooooh.....penturning!! Welcome to the addiction! lol..
You are in luck in many ways, there are a number of exceptionally good pen turners in the club as well as in the hobby that are happy to share their ideas and interests. I've been turning pens for most of the time I have been using a lathe, starting with the basics and progressing through the hobby to advanced bespoke pen making. Trial and error will drive your quest, as well as your advancing skills that just push you to try something newer and more challenging!
There are lots of options in pen kits, inks, finishes, tooling, and materials that you will work your way through. I started with Slimline ballpoints with wood blanks, progressed to acrylic blanks, then moved forward to more advanced kits using multiple different materials including roller balls, gel pens, and now fountain pens. I am now at the point that I cast my own blanks, and make my own components from scratch (with the exception of the fountain pen nib and converter pump). I don't regret any of it.
My best advice - learn, read, watch videos and do some practicing before you buy a thing. Mark Dreyer as well as our own member Barry Gross have excellent YouTubes out there showing many techniques and methods. I recommend both highly. Mark has a 10 part series that address a number of different techniques and approaches to pens that is excellent.
You will learn different chucking methods (mandrel vs between centers), materials (poly vs acrylic vs wood vs lots of other stuff), finishes (oil vs lacquer vs GluBoost vs friction polish vs lots of other stuff), ink distribution methods (roller vs nib), inks, turning shapes, and on and on. Try a little of everything if you can - try not to do one thing only until you get a technique refined.
As for supplies - lower cost for kit pens is Penn State Industries (PSI). Higher quality and cost is Berea and Dayacomm (carried by a number of resellers like Craft Supply and Exotic Blanks). I would stay away from Woodcraft or Rockler, as they change styles frequently and it becomes harder to get parts for them if you need it unless they are sourced from Berea or Dayacomm.
Good suppliers to look at - Exotic Blanks, Penn State, Craft Supply, Turners Warehouse, Arizona Silhouette, and a few like them
Good sources for info - International Association of Penturners (IAP), You Tube (Mark Dreyer is my favorite), FaceBook Pens, Turning, and Learning page. there are lots of other forums on Facebook....
Have fun with this! I am happy to help if you need info or have questions.....
Kevin