@Axsilver 32x23 size would be the minimum, larger is better. Here are some new ones that my bird (also a grey) would love.
Avian Adventures Mediana Playtop Bird Cages in White | Petco
Avian Adventures Grande Playtop Bird Cages in White | Petco
1. size. bigger the better. They need to be able to spread their wings. 32x23 is really the minimum
2. style, playtop or dorme. I actually had 2 cages for awhile, one dome top, one play top. The dome one was bigger but when ever she went in a cage to play, it was the playtop. I think it was because it was easier to hang upside down, greys like to hang upside down and attack (noisy!) toys. great fun for them. She also likes to strut on the ladder of the play top and around the the playtop itself.
3. Condition. If buying used, watch out for chipped and peeling paint. The smoother the bars are, the better for cleaning.
4. Color. I bought used and missed out on a really cool blue one, now I am glad. Birds are messy and the white always appears cleaner.
5. Feeder doors and bowls. Greys are partial ground eaters, the playtop is good for that, but she will throw her bowls around and off. She has three feeder doors, two would be the minimum that I would want for her. She only drinks water from the bottom of her cage, I would prefer it in one of the feeder doors as she throws it about once a week creating a giant mess. But she wont drink up in the feeder doors. What Louise wants, Louise gets.
6. Bar spacing, there are minimum and maximum recommended, I don't know the specifics. Louise has 2 sides with horizontal bars, and 2 sides with vertical bars. She can climb both but when she carries food around, it is always on the horizontal bars so she can more easily use her (partially filled) beak.
7. Vertical height of the cage. Big as possible but also think in terms of practicality. Mine is more like the first link, I like the shelves for storing paper. The second one would make it very easy for her to get down on the floor, and that is already a battle. Louise can fly where ever she wants (no hot cooktop landings, she is locked up until it cools). The floor is just dangerous, she can get at cords, outlets, shoes....and worst of all, she could easily be overlooked and stepped on. I also have more trouble controlling the dogs if she gets on the floor where they are at. They are pretty scared of her but even with that she is in serious danger.
8. casters. They should be attached and easily roll. Louise's cage was bought used, it does not easily roll and if I want to take the cage outside for deep cleaning, some fall off so they have very ugly tape to keep them in place.
9. Bar strength. don't buy a flimsy new or used cage. The stronger bars are better for holding up over time, not getting bent, and for ease of cleaning.
10. Aluminum vs steel. Louise has aluminum travel cages and I love them. But I prefer the white powder coat for every day, easier to clean. The aluminum cages are stunning and pricey.
11. Seed catcher. I think they are more of a difficult to clean poop catcher that make the cage bigger to place in a room. I still wish I had them, they would limit her climbing down to the floor or down to chew on the papers on the shelf. Floor playtime is good, I just want to be more in control of it.
I actually want to buy Louise a new cage as hers has an area where the powder coat is gone. Will be interested in what other have to say. If i were to buy today, it would be the first link.
Also consider a play top. Louise has these two:the first one is her sleeper area in my room. Ok, it is for her to play on when I nap.. she prefers the java tree. Either one can be loaded up with toys.
Avian Adventures Recreation Center for Birds in Platinum | Petco
A&E Cage Company Single Java Tree Stand, Small | Petco
I used petco links only because they were the easiest to find. shop around for price. watch out for shipping charges. I think I hear wayfare has the best prices during sales. Thoroughly clean and sanitize anything bought used. People won't necessarily be truthful about why they are selling a cage, an if the previous bird died from something contagious, it puts your bird at risk.
Whew, that was long!