Steve & Ron,
Before you splash out at all, may I suggest you have a read
hereOne of the premier sites for info on lathes of all types.
One thing to bear in mind is that
turning is highly addictive even more so than pens!!.
You may
think you are buying a lathe just to make and repair pens, but there is the dreaded "I wonder if I could also...."

If you are sure it's purely to make and repair pens, you can get away with something relatively simple and inexpensive.
Ron mentioned threading, and if you are going to go this route be sure you check the range of threads you can cut, some are quite limited.
Just as a quick example of range, I have three lathes. A Record No 4, modified considerably. A little Carbatec (same spindle nose as the Record) and a Myford Super 7.
The Carbatec is cheap and cheerful
see here and should be available around $250.
The Record will swing 32" diam and will come in around $1500.
Neither of these are equipped to cut threads, but with a little practice you can chase threads by hand (as mentioned elsewhere in this forum). I got away like this for nearly 20 years before I could afford to splash out ton the Myford.
The Myford is a fully fledged machine lathe, but I suspect, bigger than either of you would want* and would probaly be a bit of an overkill. You can have a look at it in my workshop
hereI chose the version without the automatic gearbox, so that by setting the gear trains as necessary threads of all types can be set up.
One of these in excellent condition can be found for around £2000 if you poke about, and it will do your great grandchildren

Main thing is to read, read, then do some more reading before you buy.
One final thing - there is no known cure. Be warned

Regards,
Ruaidhrí
* This is not a "mine is bigger than yours", just that pens are only a very tiny part of my turning interests