If you do decide on a lathe, I highly suggest
www.sherline.com as this is all they do is manufacture lathes and milling machines with all the accessories.
here is an example,
however, I am not showing how I am tapering the mast. I am tapering just using a coarse sandpaper and or a shaping tool to help get it started.
There is nothing wrong with using a drill and sandpaper as mentioned in the fore post. I have done this before. It is all up to you and what you can do and what you can afford. Good results can be obtained from many methods. I even used a MINI plane to taper my yards and mast when I did not have a drill nor a lathe.
It was all done by hand !!!