That really depends on how much time he'll spend in it.
Roughly 2x3x3ft is a fairly common cage size that I would say is the absolute smallest appropriate for a conure - this could be okay if they were out of the cage a vast majority of the time, but not so good if they spend the day in their while you're away at work.
It would be hard to be too big - but keep in mind a bigger cage is much harder to clean. You want a size you can commit to keeping clean for him/her.
Bar spacing is another issue - shouldn't be so wide that they can get their head between the bars - very dangerous if they can. Also be aware of coatings or materials - very few if any reputable sources have cages still coated with anything dangerous (zinc, etc).
In addition to spacing is bar size itself. A conure can do quite a bit of damage with their beak. I suspect most conures could chomp right through the thin bars common of parakeet/finch cages.
Take a look at the latches/closures as well. It's amazing how good conures are at opening cages, or completely disassembling them if they can get at the nuts and bolts.