Welcome to the forums and to the world of bird ownership. I have only been a parront for a month, but I think I can give you some answers as a fresh bird owner, as well as my impressions so far. I defer to the more experienced owners for more in depth answers.
The best diet to feed your GCC would be a combination of a good pellet diet such as harrisons or zupreem and fresh fruits and vegies. Always look up a food before giving it to your bird though. Avoid seed mixes, as a seed diet is basically the equivalent of a human eating candy bars for every meal. That being said, GCC's love spray millet, and I've found that a nibble of that is a good initial reward for training.
While I believe that, given a safe environment and good diet, GCC's are hardy little birds, they are an exotic pet. I live in a more rural area in Florida, and finding a vet that did more than nail trimming for a bird was difficult. To give you an idea, a nail clipping and a regular physical for my GCC cost me near $100. That did not include blood work. I imagine, like with all pets, that illness means dollar signs.
The best type of cage for a GCC (or any bird) is really the biggest you can afford and have space for. Make sure that the bars are not too spread apart that you think the head can fit through. Certainly, you want a cage where the bird can spread its full wingspan. Make sure there is room for plenty of toys as well.
The best toys for a bird is really subjective to the bird, but in general there are four types of toys that you should incorporate into your bird's life. A foraging toy, a destructible toy, an auditory toy, and an exercise toy. Other people may have different opinions, but i think this is a good start. In the wild, parrots forage for food all day. Finding a toy that makes them work for a food reward stimulates that instinct. My GCC loves toys that he can shred to pieces. Getting your parrot a destructible toy can help save your stuff! Parrots are also auditory creatures. Having a toy that makes noise when interacted with is often engaging and fun. Finally, and exercise toy does what the name describes. Foot toys (my bird has a parakeet barbel foot toy that he loves to throw around), and swings are good examples.
Parrot proofing is a very complicated thing. Think of everything you don't want your ferrets getting into, and then realize that (if flighted) your bird can get anywhere. Mostly, look around your house for chewable items or dangerous aspects. One thing I had to break my wife of was scented candles and air fresheners which can be deadly for birds. I smoke a pipe from time to time outside, and have to make sure i wash my hands and change my clothes before handling my bird. Also, if you use non-stick cookware, make sure the bird is not in the room as the fumes are also harmful.
Training with my GCC has been fairly easy. He did already understand step-up when I got him, but I immediately started with target training. His attention span runs between 5-15 minutes depending on his mood. In three weeks I've managed to get him to wave and spin in place. Your mileage may vary.
Ah poop. Yes my GCC is not yet trained in that area, and he poops regularly and indiscriminately. Luckily, he is a small bird, so there isn't much to it. When he gets scared, he poops, and I have to constantly clean his desk perches and my shoulders.
The cage should be cleaned at least once a week. I usually spot clean his cage each day. I check his toys, perches, cage bars and sides, and the floor around it, and wipe up anything that missed the tray at the bottom. Then, at the end of the week, I do a more thorough scrub, and change the bedding. He never smells, and on his cage's worst day I didn't really catch an odor. I would think that even if your ferrets are descented, that they would smell far worse than a GCC. My GCC is a really adamant bather as well, which is why he needs new water constantly.
Hope I could help. Hopefully, more veterans will add more details for you. Good luck!