Not a whole lot are connected but some story's are in very little ways. It would have a little box that refer you to another issue to give a little more to the story, but most of the time its not really needed that I have read. If you can't get the first couple or so issues. DC been coming out with Graphic Novels with the first story arc.
Detective Comics (Have to read #1 because it so great)
Green Lantern: New Guardians (Story so far is very great and fun)
Red Lanterns (Love it a lot)
Batman Incorporated (Really a fun reader)
Earth 2 (Really different superhero origins in a Earth with no superheros)
I am looking for comic book storage that is unique/different then just having a bunch of boxes laying around on the ground. I have seen wooden comic book drawers but they cost too much and filing cabinets look ugly. Post pics if needed.