There are a wide variety of bags that are used as an EDC bag. Messenger bags, backpacks, shoulder bags, brief cases, pouch sacks, etc, all can be used depending upon one's concerns for quantity, organization, not drawing attention, blending in, and weight. I've tried the shoulder sling bags, and messenger bags, and personally prefer a backpack style EDC bag.
Bags come in a wide variety and configuration and also price ranges. I cannot emphasize enough to buy quality products. Get the best you can comfortably afford. A strong, not too heavy bag will last and should become more comfortable with daily carry and use. Always remember that if you use something from your edc bag, that it must be replaced as soon as possible. In this way you will normally have your tools/supplies on hand when you need them again. I think every individual owes it to themselves to experiment and find out which bag suits their needs on their own. This way you develop familiarity with what you have and how you have stocked it inside your bag.
Here in the city, we have to carry practical items and we unfortunately don't have firearms to consider. I've posted a list of some general things to carry in an EDC bag. This is a partial list, other folks may add or subtract things depending upon what they consider to be important.
flashlight
knife
keys
walkie talkie (optional)
multi-tool
first aid kit
phone
bandana
note pad
sharpie
spare batteries
water
snacks or food bars
emergency poncho
fire starter
That is a good list to start with. Good luck!!