Hi Elaine
The basics required are a mandrel and possibly a trimmer**. most of the other items in a kit can be bought as you go.
Each different pen kit, slimline, sierra, etc require different sized bushings and drill bits so one usually purchases these with the first purchase of each kit.
The stuff required for all pens that you may have already is..
gouges: standard size is fine, mini pen sized gouges not required.
glue: epoxy, CA or PU
abrasive.
finish: friction polish, CA, MC wax, etc
potato or plasticine for blocking the tubes
And for the first pen you turn..
pen kit
bushings
drill bits
mandrel
pen trimmer***
order of play is
make/take timber pen blank, lets say 150mm x 20mm x 20mm
cut to length: 2 or 3mm longer than brass tube.
drill blank: with correct sized drill* (too tight and you may split the wood and too loose will result in off centre or not sticking.)
optional: clean brass tubes with acetone or similar and sand lightly to help adhesion.
plug brass tube ends with potato or similar. (you dont want the glue inside the tube). Wipe again with cleaner.
coat tube in glue and insert into drilled blank, twisting as you go to spread glue. make sure brass tube is pushed below the surface of the wood. you will trim down to the tube later.
set aside to dry.
once set, remove potato and using barrel trimmer gently trim to just above brass tube.
put appropriate bushings and blanks on mandrel and turn to size (just a fraction bigger than bushes)
sand
polish
remove from lathe
assemble as per instructions (bench vice with soft jaws will be fine)
write!
fine tuning will come with practice (using calipers instead of relying on bushes for accuracy etc)
*Apart from the slimline 7mm kits, the majority of the pen kits seem to be imperial and do not always have an exact size metric equivalent. UKdrills is a good source for cheap imperial and metric bits.
**The barrel trimmer will need to be a close fit inside the tubes. You can get multiple shaft sizes for the different tube sizes or, as i do, use the std 7mm shaft in conjunction with 7mm tube with timber turned to the correct size (usually made from early pen making attempts turned and sanded to size)
***or you can use a sander if you can guarantee you can hold the tube absolutely square to the tube end.