I'd go at least 26"x 20"x 34" on a regular bird cage or 32" x 24" x 40" for a flight cage. The major difference is the regular bird cage will generally have feeder doors, small door to let you change food and water bowls without having to put your hangs in the cage. Where as most flight cages do not have feeder doors so you have to reach in to change the bowls. Well both my guys are very cage territorial and sticking my hands in BB cage is somewhat akin to stick my hand in a running garbage disposal, yes I will be bleeding when BB is done with me. I had Riti, my little Kakariki who passed away last year from cancer, and it was never a problem with her but Conure's are a lot more aggressive. I plan to buy another cage like I have Cheddar in when I move to Tampa in June (I hope it'll be ready then) to replace the flight cage BB's in.
I have learned in almost 20 years of having birds that buying too large of cage can be just as bad as buying too small a cage. A large cage of equal quality will cost more, sometime much more. The bigger they are the harder to move around they are, and big cages can be a real PITA to clean. Match the cage to the bird. Cheddar is fine in the 26" x 20" x 34" cage and as plenty of room certainly when he's out most of the day. I had Nibble, Tiel, in a 32" x 23" x 50" parrot cage and he was lost in it, he just sat in one place. He ended up in a cage the same size as the one Cheddar is in with two other Tiels and they are all happy, but they do get lots of time out.