See my post #3 in this thread:
If you buy high speed steel (HSS) tools, be sure you have a way to sharpen them.
Here are the turning tools I use for pens. The HSS tools come from the Sorby six piece turning set, and the carbide tools are the Rockler full size ones:
Sorby HSS Tools:
* 3/4 inch Spindle Roughing Gouge (843H)
* 3/8 inch Spindle Gouge (840H)
Optional, but I use them on pens:
* 3/4 inch Standard Skew Chisel (810H)
* 1/8 inch Parting Tool (830H)
Rockler Full-Size Ergoniomic Carbide Turning Tools:
* Square Radius
Optional, but I use it on pens:
Used to round off the sharp edges on plastic / acrylic pen blanks to reduce the chances of chips, catches, and cracks when roughing down to a cylinder.
* It is okay to switch between tools or switch between HSS and carbide tools
I do not limit myself to one tool for one pen. I go with whichever tools work on whichever material I am working on that day. Some days I will use one tool and it won't work, so I switch to a different tool that cuts perfectly. The next day, it will be the exact opposite. Sometimes the HSS tools aren't sharp, so I use the carbide out of laziness. When the HSS tools are sharp and cutting well, they are a joy to use.
Some tools just seem to work better on certain materials. I sometimes struggle with the HSS tools on those very hard plastics/acrylics, but the carbide tools cut well on them. Most people expect you to use carbide tools as scrapers. I do that, but sometimes I use the carbide in bevel-rubbing mode, especially on plastics/acrylics. To my surprise it can work well, with the material peeling off and floating away in very long, very sensual, ribbons of plastic. (... or wrapping around the pen blank in a cotton-candy-like mess that must be stopped and brushed off to continue turning.)
The quality of your turnings can differ between tools and much of it depends on your skill level. Some tools make it easy to leave very smooth, no-sandpaper-required finished surfaces. Other tools require more post-processing with sandpaper to be finish ready. A skew chisel can leave an amazingly smooth surface ... or not. Practice helps.
* Optional HSS Tools
A skew chisel can be a wonderful, versatile turning tool in the right hands with practice and acquired skill. I am still learning to get better with the skew chisel. I wonder whether my battles are sharpening issues. When the skew chisel is cutting well, it is a wonderful thing. When it grabs and catches, well, not so great. My Sorby skew chisel has sharp, square edges along its length. The current version has rounded, softened edges to make rolling the tool easier. Someday I may have the thrasos to round the edges neatly on my own skew chisel, or perhaps I will treat myself with an oval skew chisel.
The parting tool is perfect for making tenons, which is needed for a few special pen kits. (I have also used the carbide diamond tool to make tenons for pens.) The parting tool is so useful for other turning projects. I use it often, just not often for pens.
* Optional diamond carbide tool
If you have only carbide tools, then you would use the diamond tool to make tenons, which are uncommon for pens. An HSS parting tool might be easier and arguably better for tenons, but the diamond tool is certainly up to the task. I use the diamond tool to turn finger-grip rings on pens. I could easily use a HSS skew chisel or parting tool instead, but the diamond tool just works for me.
* Full size vs. mini size vs. pen size for carbide tools
I like the size, heft, and feel of the full size carbide turning tools. They are useful for more than just pens. The problem with the full size carbide tools is that their tips are larger, so turning fine details on pens is more challenging. You might prefer mini carbide tools or even the smallest pen tools. One issue with the smaller tools: They don't always come with the same tips. The Rockler mini set has a diamond carbide tool, while their pen set has an HSS parting tool instead.
* Tools I don't use for pens
I do not use the bowl gouge, round nose scraper, other hollowing tools, etc.
* Great resource for learning more about Pen Turning
There is a wealth of information about pen turning at:
EXAMPLE TOOLS, IMPORTANT NOTE, PLEASE READ:
Here are links for the tools that I use, for your reference and example. They work for me, but PLEASE don't feel that you must acquire the same ones. I tend to buy from Rockler because they are my local woodworking store. There are many other companies that make excellent turning tools. You can find turning tools at all quality levels, including tools that are worse, and equal, and better than mine.
Robert Sorby Six Piece Set:
I bought the Sorby set when it was on sale at Rockler, but it is out of stock right now. It came with a GREAT woodturning book and an okay DVD. You can find the set elsewhere at lower prices. The book and DVD can be purchased separately.)
Rockler Full Size Ergonomic Turning Tools - Carbide:
Also consider their mini tool turning set or their pen turning set.