Hi Hilary,
1= playtop v dome, personally i prefer playtops, gives additional play area but it is personal preference.
2= Corner v rectangle, rectangle cages seem to have a larger width than corner,personally i would but a cage that has a greater width than height.
Always go for the biggest cage you can afford for your grey.Here is a link for other members cages & you can see how they are set up
http://www.greyforums.net/forums/african-grey/11611-post-pictures-of-your-cage.html#11611