Small to medium sized wood lathe is what I use, something with a 2 morse taper for projects other than pens like bowls etc.
However, lathe is less important than good sharp tools.
Don’t forget that blanks need to be drilled. There is no better way in my experience than on the lathe itself - best purchase I ever made was a set of pen jaws for my chuck. So a decent chuck package also important.
Below is a lathe and chuck package that I started out with.
[URL unfurl="true"]https://www.norfolksawservices.co.uk/products/machinery/wood-turning/wood-turning-lathes/nova-comet-ii-dr-lathe-g3-chuck?gclid=CjwKCAjw0N6hBhAUEiwAXab-TezSCdpX4gfJpQnS-hYO5PC9Qqnz8hFYMxapURg1Yfd3CLMoi2kT-RoCe88QAvD_BwE[/URL]