Colin, welcome to the forum.
If you are just starting and don't want to spend a lot of money initially here's my recommendation;
Find a single barrel kit that you like and buy a couple plus the bushes and more importantly half a dozen spare tubes for that particular kit.
A lot of people start with Slimlines/Streamlines, but they are not the easiest.
Gather up old chair/table legs, odd bits of timber.
Practice squaring off the blank and drilling straight for the tube.
Practice turning to the bushes and getting used to the tools.
Practice finishing techniques.
If you make a cock up, just turn the timber off the blank and start again.
Everything that you turn doednt need to be made into a pen!!!
Find a turning club and make friends, especially with a pen turner who can help you!!!
Ask plenty of questions!!!