If you're looking for something to do while you wait for that lathe maybe you could decide what joint pin you're planning on using. Then you can figure out what taps and drill bits you need. If you're going to use weight, that's another drill bit and tap, probably long ones. I don't build cues, I work on my own stuff and it's amazing how much stuff I've bought and I stick to one joint pin and one type of weight.
If you're going to want to use thread on ferrules you'll need a compression die and a tap for that.
And given you're going to be waiting you can order a lot of this stuff from cuefits on ebay, takes a while to get from china but it's a pretty inexpensive way to get them, and you have the time.
Also boring bars, quick change tool holder, a good drill chuck, parting tools, etc.. You'll need a way to cut wood to length, initial turning from square to round. I'd suggest buying another lathe for initial turning.
The mid America lathe is okay for working on the ends of cues, but I wouldn't want to try to build a full cue on it. If I were going to attempt it, I'd buy a second carriage and modify it to run on a taper bar.