Which chisel did you order Peggy?
So far all I have used to make a pen is a spindle roughing gouge and a 1/2 inch skew. But I will be the first to admit that I am very new to pen making and indeed, wood turning so this may not be ideal. The general vibe I have picked up is that you need to experiment a bit and adopt whatever works best for you personally. What works for you, may not work for me and what works for me, may not work for the next turner along the line.
You will need pen blanks, or some way of cutting wood into blanks of a useable size, a bandsaw seems to be the preferred method for most. Also a way of holding the blanks so that you can drill a hole square through the centre lengthways. I have a drill press and a drill press vice for this, but with care a hand/cordless/power drill could be used with a pair of large grips/bench vice or even just a few bits of wood screwed together to make a jig. You will need a pen mill to square off the ends of your prepared blank (this will likely be included in your mandrel kit) or failing that a disc sander can be used with a little practice. Glue to set the tubes into the blank, CA glue for speed or epoxy if you are prepared to wait overnight for it to cure.
For the turning part, everything you need to mount the blanks should be included in your mandrel kit. Obviously the mandrel, correct size bushes to hold the blank in place and guide you to turning to the correct size. Also whatever finish you have decided on. As above, I use a spindle roughing gouge to get the blanks round and roughly down to size and then I use a skew to work in the final shape and clean them up. I will admit that the skew is not the easiest of chisels to use though, so maybe a spindle gouge may be better. For final sanding I have various grits from 80 grit (which I rarely need to use) through to 600 grit which should be smooth enough for a finish to be applied. It looks like you won't, but if you decide on a "plastic" finish such as CA of lacquer then Micromesh pads from 1500 through to 12000 would be a good idea.
For putting the pen together you can indeed use an assembly kit, though to be fair I think this is unnecessary if you have a bench vice, but that is just me.
All the above works well enough for me personally, but I expect that others on the forum can offer alternatives that may work better for you. As above, just get stuck in and see what works for you and above all, enjoy it!