African greys are so smart and they needs lots of stimulation! Tons of toys, a huge cage and time outside the cage or they get bored and may feather-pick themselves bare. It's really sad to see They also tend to bond with one person from what I've heard. Personally I've had cockatiels that weren't as demanding, but then again, probably not as rewarding as having a grey. Those birds are amazing...the best talkers of all the birds, and they do live a very long time, so it's a lifetime commitment! Birds, in general, are loud and noisy...so that's something to consider. My one cockatiel was quite loud and made quite a mess, but he was a sweet little guy. Birds do sleep at night...it's best to cover them with a dark blanket so they stay quiet.
I'd be more worried about the cat getting hurt by the grey than the other way around Those birds are tough!
I hate to be "Captain Bringdown" here but African Greys are a TON of work-they are mostly compared to 2 yr olds. They require a lot of daily attention and if not given that then they tend to be feather pluckers and start having behavioral problems. I have been a vet tech for 9 years and have yet to see an African with all its feathers. We have 2 lovebirds and although they are adorable to look at, they unfortunately do not come out of their cage very often as they have bonded more with each other than us. I would advise against them knowing what I know now because they are the loudest of all the small parrots-don't get me wrong I love them but they can get quite noisy at times. We also own 10 cats and an 11 week old Chihuahua so the house is pretty full which is why they do not come out of their cage ever unless for a vet visit or a thorough cage cleaning.
Whatever you do choose I would do a lot of research on different breeds as well as talk to a local vet in your area that sees birds and get their opinion on what bird would best fit your lifestyle and desires in a bird. Good luck and let us know what you get and cannot wait to see pics!