To what extent do you expect to be able to do repairs. Is it just tips and shaft work, or more than that? Just tips and shafts, the basic Mid America cue repair lathe $900 does a great job. More than that, you will need a lathe with a lg bore and bigger motor like their professional lathe $1600. Of course there will be more than that you will probably want, figure a couple hundred bucks to start and up from there. It's addicting, even if you don't want to do work for others. There are other similar makers of similar equipment.
The old saying of buy once cry once is true, but in the case of lathes like these, there is a strong market to sell your lathe if you decided later to move up a level, even if trying to sell without shipping. When I posted my standard repair lathe for sale on this forum, I had multiple offers from all over the country, and some up to a 4 hr away drive willing to come pick it up. They are not hard to resell, especially if you are reasonable in your selling price. I moved up to their Professional version and it will do most everything I need it to do. I do wish I had a machinist metal gun lathe though, but at about 10k with accessories, that's getting up there to just play around with.
What I really wish for would be if they could make a zeroable chuck to zero out the runout on these Mid America type lathes easily like they have for larger lathes.
