You still need a very large cage--- it is just that depth and width should be your focus--- yes, you want a cage that is far off the ground and has a bit of height for climbing, but horizontal space and depth matter most, so a "large cage" may not be as large as it looks if the majority of the space is vertical. A corner cage can be fine as long as it is very big, but lots of people dislike the corner part because it makes setting things up difficult and can go unused (hence the waste-of-space statement). Do not look at smaller cages...but if you ask a lot of people, a rectangular cage is preferable.
I would definitely get a cage that has a seed-skirt and a removable grate and removable tray, plus a solidly latching door with reinforcement latches.
Also make sure that the food doors are in logical places and that you have at least 4-5....a large door should also be high on your list as it makes access/cleaning/toy attachment easier.
***NO ZINC, LEAD OR GALVANIZED METALS*****Stainless is the safest , but if you get a painted or powder-coated cage, make sure it is made in the USA or be prepared to call the company and find out what metals are in the powder coat and iron underneath it (as powder coating can and does wear off with a bird this size).