For me, I didn't realize how important certain things were until my wifey bestowed upon me in 2002, a Powermatic 3520. With a swing over bed of 20", and tail to headstock of a little over 34", I thought I would never outgrow it. Then came the time when I found the big wood pile that my town puts together for people to pick firewood out of, and the curly and burl that was mixed in.
But seriously, here is my list of the most important things, assuming that the lathe is well built, center to center is dead on, and it is heavy enough to not walk across the floor. Not necessarily in any order…
1. Without a doubt, for me, variable speed. My lathe has two main speed categories that you set with a belt move, then the variable speed drive takes over. There is literally nothing like having a lathe that will rotate at maybe 15-20 RPM while you inspect the work, see if you are mounted correctly, or maybe actually mark a section with a pen. And having variable speed for not only turning, but buffing and polishing, it's kind of like the first time you drive a hydrostatic drive lawn tractor. You never want to go back.
2. Ability to change out chucks, heads, tailstocks, etc, without taking 5-10 minutes out of the project. this includes through chuck with a rod.
3. My lathe has a movable head. This seems like kind of a not-needed, but I can center it on the bed for short, big pieces, and it helps balance it out. I can also turn my head around so I can do really big stuff off the end, if I so choose. (You need a separate tool rest stand for this - I own the Powermatic cast iron unit)
4. Reverse. What a wonderful thing when you are polishing and buffing. It also comes in handy when you want to do that reverse cut where you cannot quite get the tool where you want it. The reverse direction of the variable speed drive opens up all kinds of opportunities for different kinds of cutting, polishing, all kinds of options.
These are the biggies that I use.