I feed my little GCC Zupreem natural food, and he loves it. It's a natural pellet food, and it's much MUCH better than a seed diet, because they won't get all the nutrients they need from a purely seed based diet. I'd also suggest feeding fresh fruits and veggies like spinach, broccoli, carrots (Tori adores carrots) etc. I have a list of what's good to give them somewhere. be sure to check if what you're planning on giving them isn't toxic before you feed it. For example, avacados, I believe, are toxic to the little guys. Obviously, make sure your bird always has fresh water.
Make sure you give your little birdy as much out of cage time as possible, and train him/her while s/he is out. My GCC seems to have ADHD and only can pay attention for about 10 minutes at a time before he gets bored or distracted.
Start socializing with your bird as soon as possible. I offered treats thru the cage bars until he would consistently come and take them from me, then I opened the cage door and offered them directly to him from my hand. I also used target training as a type of socialization because he has decided "touch the stick" is his favorite game. (Basically you just take a stick, I use a clean disposable chop stick, and stick it thru the bars of your bird's cage. when they touch it, click, or say good bird, or w/e you want to be the queue that the bird knows means they are getting a treat. Then give your bird a small treat for having done well, let them eat it, then repeat somewhere else in the cage.) It's a nifty trick for getting your bird to go where you want them to if they aren't quite comfortable with stepping up, or with you carrying them.
An important thing to know before you get your bird, is that you want to not accidentally train them to scream for your attention. If your bird starts chirping loudly at you, or screaming, leave the room, wait for him/her to calm down, then come back. Sometimes they do scream for other reasons. Like, for example, Tori decided to be particularly fat one day, and ate ALL of his breakfast in one go. He usually has a mid-day snack left over, but not this time, so he started screaming at me to give him more food.
As for the cage, usually bigger is better, but make sure you get one that will last a long time. GCCs can live for...what...40 years? You want a cage with about the same life span. Having a small travel cage for vet visits is a good idea, and a smaller sleep cage is another option too.