If you already have an AXA or can find one cheap, it will work fine. Otherwise, I would pick BXA. Why? It takes larger tool holders, so there is a better selection of tooling available. A lot of people also like the Swiss Multiquick 40 position toolpost. I believe that is Ross' favorite, perhaps he will provide details. For a live center, I like the Bison 2MT set with several different styles of center. e.g. https://www.ajaxtoolsupply.com/bilicemtcela.html
Don't be scared off by that price, if you search around you should be able to find it on sale for at least half that price. If you buy a 2MT dead center, make sure it has flats on each side of the small end of the taper; otherwise it might not fit the tailstock. For a tailstock chuck, its hard to beat a Jacobs ball bearing chuck. I have a few Aloris chucks too, but I've more problems with them than the Jacobs chucks.