When initiating a new Comp, you choose a size and aspect ratio for the page. Adobe supplies a bunch of presets for popular ones.
Comp is based on the theory that you want to start as if the blank page is a napkin, using gestures to scribble predefined object types that are subsequently replaced with text and objects.
It's not as faithful-to-tradition, but you can also just choose objects and placeholders to put on your page without the fancy scribbling recognition.
Comp CC uses the same color picker and palette handling as the othe Adobe apps. If you want to organize them, though, you have to go to Color CC and create libraries for each set of color themes you want to use. ("Color Themes" is the name of one of my custom libraries.)
Comp CC supports jumping directly out to Typekit to search for and sync typefaces that you haven't previously set up for on the desktop, and it will sync them back to desktop applications.
Your crop options are rounded rectangles, rectangles or circles/ovals.
Line and letterspacing controls are a nice surprise.
While the ability to hand off a Comp directly to a desktop application is nice, it's not optional. You can't save the native file out any other way, just as an image.
These are the various ways you can get images into the app. The placeholders come in round or rectangle and you can simply tap one to fill it with an image.