Half inch is good. A greencheek is closer in size to a large budgie, so you want to go with 1/2" or 5/8" bar spacing.
As far as cage dimensions, bigger is better, as long as the bar spacing and other openings are appropriate. I keep my greencheek in a 30x30 cage. I wouldn't get that one again. Being square, it won't get through my doorways. 30x24, would be more practical if doorways will be an issue for you. You want to be able to get the cage outside to hose it off, and stuff like that.