Nigel, welcome to the forum.
If shopping for a lathe you should be looking at one with a 2 Morse Taper and variable speed control.
Pen jaws and compression mandrel are recommended.
I did very little turning before making pens and started using carbide tools until I became more proficient with woodturning chisels. I am still using carbide and see very little wrong with them. Your startup cost will be a lot less with carbide than chisels and sharpening tools, but it's your budget and your choice. Others may steer you towards chisels which may well do a better job if kept sharp and I would not disagree with them.
Enjoy your new hobby.
Alan
