The issue with greys and becoming frightened in cages seems to stem from the fact that they are usually, but not always, clumsy babies and youth. If they fall, and it scares them or hurts them, then they will tend to become overly cautious. I have known of a few greys who became so terrified that they would only sit in one small part of a cage, but that is excessive and not the norm. However, it does happen, and I have personally seen a grey who was like this.
Many greys do live in 3' wide cages. This is actually the size that you will see most often recommended. Therefore, I do not believe that is a bad size for a grey, but they are also individuals, and some prefer smaller cages. I think much of it is what the individual bird becomes used to. Additionally, I would think that a tall cage would potentially cause more fears than a long cage, because I would assume that the bird would be afraid of falling a longer distance as opposed to being afraid of going from side to side, but, again, this all depends on the individual bird.
Ashlynn herself is in a cage that most people would consider too small for a grey, but she is very happy. I got this cage thinking I would get her a larger cage when she was a year old and not as clumsy, but I may just keep her in it because she is very content. I did put my senegal, another African bird with a similar personality, into a larger cage, and she never got used to it and would just sit in one spot and not play. After many months, I moved her back into her original smallish cage, and she is very playful and happy there, so I have no doubt this could happen with a grey, too.
It is often suggested to start baby greys out in smaller cages and then move them to larger cages when they are past the clumsy stage, but then you have the issue of the fact that they have learned to like the smaller cages.
Does the cage you like have a divider? If so, you could always start a baby out in one side only of the cage. I would use the side that is under the playgym on that particular cage because it is not as far to fall to the floor there. However, your baby could love the entire cage right from the start. There is just no way to tell until you try it.
If you want that cage and you start the bird out in that cage, I think it should be fine. My only issue with those types of cages is that they can be hard to clean, but, the one in the photograph has two big front doors, right? If you have a door in front of both sides then the cage should NOT be a problem to clean.
I would, however, follow the following advice from my avian vet. Do NOT trim a baby grey's nails as much as you would trim other birds' nails. Baby grey nails should be a bit uncomfortable for you when you hold the bird. This will help prevent your baby from falling in his cage and developing fears of falling. Greys are very heavy bodied birds and they fall easily and it hurts.