You definitely at a minimum want at least 2 lathes capable of cue work. If the repair does not keep one lathe tied up all the time, It will still get in the way when trying to work on building a cue, and repair comes in, taking priority. when you get a steady flow It becomes near impossible to work on builds. Breaking down a setup that's dialed in, and having to continuously dial It back in after doing repair work is frustrating and counter productive. For me the more lathes the better, because I'd like to have several dedicated lathes to do specific tasks, but It's gonna take me some time to get to where I will be satisfied, and I'm also gonna need a larger space to house all of the equipment. I'm Working on It though, trying to finish up another lathe right now, but the dog on metal supply place is taking their sweet time shipping the metal I need to fabricate My motor bracket. I paid for It on the 3rd of this month and still have not received it. Hopefully It will come in this week and I can finish up on getting that one operational.
If You have the funds and the space then I would recommend having at least 2 lathes, but if your not sure that You will stick with doing this, then maybe 1 capable of doing both repair and builds would be better to start with, get Your feet wet, and see how It goes. There's also a lot of cash that goes into other things you need for this, that often goes unseen. Tooling, hardware, woods and other materials, not to mention common supplies. It all adds up to more then may be seen at first, and constantly has to replenished as you use up what You have on hand. That's something to take into consideration unless You have unlimited funds to spend. You also want to load up woods ahead of time when possible. Not only does It keep going up in price, but It needs time to hang in Your shop before working with it, and it also gets used up rather quickly once You actually start to work with It.
If not planning to do repair work, then I would just mention that a lot of experiences comes from repair, as well as many buyers of cues will come through that chain of work. It Also helps bring more funds back in to It, that will help bring in a more consistent income. Just something to consider.
The different operations could range quite considerably depending on the person, but dedicated lathe could consist of a repair lathe, cleaner lathe, tapering lathe, point lathe, billet lathe, joint lathe, and the list could probably go on quite a bit, but with the right setup, 1 lathe could be capable of doing It all, or a couple of them could split the tasks between them, and makes thing a little easier. It's really a matter of what You can afford, have space for, and what level of productivity You would like to achieve. When You bring cnc into the equation, things could change too, because some machines are capable of doing some of the tasks that a lathe does.
Greg