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this post of mine for some basics concerning your lathe tools ... how to sharpen them from right out of the box from Harbor Freight.
I do my finishing with a combination of Minwax Stain'n'Seal (Natural Wood color) and Harbor Freight Super Glue. (not the gel!) To prepare for this finish, I sand the wood up to 1000 grit ... I get the variety pack of sandpaper sheets of 220 - 1500 grit paper from Harbor Freight as well, since they are cheap and effective, and then I clean the blank with rubbing alcohol or acetone. Then the minwax, followed by 6 - 12 coats of CA.
Hobby Lobby has micromesh sanding pads .... grits 3200 - 12000. They are abut 2.5 inches square, double sided (same grit on both sides and marked), and will last you a good 20 - 30 pens with proper use. Cost is a bit on the high side, at about 12 dollars for the set, but more than worth it! Sand laterally (along the grain of the blank, with the lathe turned off as you turn the blank slowly by hand) at least every other grit with the micromesh. You should do the same in the previous stages of sanding as well, to remove radial lines that go around your blank. Sanding in the pre-finish stage up to 1000 grit greatly reduces the roughness of the wood and the finish that goes on top of it, which saves you time and effort with the micro-mesh pads. It also makes your pads last a good deal longer!
Find an Advance Auto Parts or other car parts shop and get some Meguiar's Plast-X plastic polish. It has super-fine abrasives that break down into finer and finer particles as you polish, taking a 10,000 grit surface up to over 30,000 .... a glass-like surface, especially one that was coated in multiple layers of CA, or superglue, but it will work on soft metals (aluminum, copper), soft rocks (turquoise, alabaster, soapstone, marble, malachite, lapis lazuli, tigereye, ect), and acrylics like alumilite and silmar.
Finally, while you're in the car parts store, pick up a bottle of liquid or paste Turtle Wax Super Hard Shell ... it goes on last, and helps protect the shine on your pen from things like fingerprints.
Keep in mind, my way is not the only way ... it's certainly not the "right" way, it's just the way I do it. You can try it and see if it works for you ... but feel free to change things around to what feels right and works for you!
Many people only sand up to around 400 grit ... finish sand their CA to 1000 grit and then go straight to some type of polish, and still end up with a beautiful glassy finish ...
Many people also prefer the look and feel of real wood, and finish their sanding at around 220 grit, then begin applying a sealer, polish it up with some wax, and call it pretty well done ...
No one person's way is more right than any other, which is part of the beauty of this form of art! If it works for you, then it's good to go!
edit: That's Crepe Myrtle...