A pic of things to come...
In order to have access to the full range of possible adventure types seen in superhero comics it is necessary to have a solid setting. As with all genres of table top, many players and referees prefer to make use of a published setting. These settings come with significant drawbacks in regards to the above mentioned goal, however. For example, your player character cannot hope to fill Batman's niche if he exists alongside batman; he can't find the Microverse or the Negative Zone or the Great Refuge for the first time either, because Reed Richards already did all that. The best PCs in such a setting can hope for is to be shadows of the established heroes.
At this point, one might ask what is meant by the "full range of possible adventure types?" The truth is writing an adventure that involves taking down bank robbers doesn't really require much in the way of world building. However, if you wish to do space, cosmic, alternate reality, time travel and/or world/universe saving adventures, having at the very least the bare bones of the greater setting in which these adventures take place will prove invaluable.
It is the purpose of this series of posts to explore and explain methods of superhero universe creation, and in so doing provide the referee with the tools necessary to create her own realty or series thereof.
Point of imformation, this will mot ne an easy process. You will have to read, and make stuff, and we're doing this my way, not in some general touchy feely fashion. I have a step by step method which is labor intesive. So if you want to do it the easy way, and it is a game, so who can blame you for wanting it to be easy, pick a piblished setting, do the homework below anyway- at least read DC's 52 if nothing else. Also, take this one peice of advice, if you use DC/Marvel the heavy hitters like Captain America or Superman or whoever should, in my opinion, be MIA presumed dead for the duration of your campaign. This will give the PCs the center spot.
Fantastic Four (1963) 1-100. Annuals 1-7. The first truly modern superhero comic. Marvel universe is more or less constructed during the course of this legendary run. It is all available on Marvel Unlimited. Includes everything you really need to know about superheroes. It is to superhero comics what the Beatles are to pop music. By our modern standards it may seem a little clumsy from time to time, but there is in fact, very little wasted beyond a few hundred words here and there. Start here.
Godland 1-36 & Finale. A cool cosmic story and an interesting and self-concious take on comic book world building.
Crisis of the Infinite Earths, Infinite Crisis, Final Crisis. DC multiverse lives and dies. Superman sings. Commonly available at libraries. The first one is really text heavy.
DC 52: a fantastic example of maybe how one could go about using original characters in a major setting.
If the list above seems daunting there are always cartoons.
JLA: Twilight parts one and two for world building stuff.
All the DC animated universe cartoons for an excellent presentation of the full range of adventure possibilities.
Batman the Brave and the Bold: another excellent example of what supers can be.
Avengers: Earth's Mightiest Heroes
Obviously you can't get to all of this at once, but if you enjoy supers you'll get to as much of it as you can as soon as you can anyway- if you have not already. If you don't enjoy supers, I doubt you have made it this far.