To give us an idea of the overall feeling of your brand, let us know which styles you lean towards
For starters, this is a bit of a rush job: I'm planning to hit a Christmas release, so I need to have finished graphics by Dec 5 or 6th at the latest to hope to get the app submitted to the App Store in time to hit that date.
For requirements: I need to get a icon that's usable as an iOS app icon, and that I can make use of on the app's website as well. So minimum size is 512x512, and it'll be scaled as needed for other sizes (if you wish to provide differently sized files for the appropriate uses, that's great, but I don't require it). A word mark to accompany the icon on the web site will also be needed, though it need not be fancy: I would rather more thought go into the icon itself.
Other thoughts: seeing as this is an app about lolcats/memes & it's for Instagram users, the obvious place I went to for the icon is something cutesy integrating a cat & a camera. Go nuts if you think that seems too obvious, it was just the first image that popped into my head.