I just saw "Deadpool" and loved it, and I look forward to seeing "Batman vs. Superman", but I've never read comics. It seems that there are thousands (right?) of them for each superhero, and there are multiple superheroes for each franchise. Sounds like there'd be a lot of time and money into reading them.
I do envy the ones who have read them, whenever it's revealed that *insert character* will be in the next movies and they all get excited.
Comic Book movies are made for everyone these days, so it is very common nowadays to love comic book movies but don't read the comics. I've read some comic books, mainly the Marvel comics that were Written by Stan Lee and drawn by Steve Ditko, John Romita Senior, John Buscema and Jack Kirby in the 1960's. The comics they produced are the classics stories that set the standard for all comic books to come, and personally, not one modern comic book could compete with anything they produced. So, if you want to perhaps try some comics out, try out those written by Stan Lee and drawn by Steve Ditko, John Romita Senior, John Buscema and Jack Kirby in the 1960's. Their stories were new and fresh and easy to read and easy to understand. The new comic books however are made for hardcore comic book fans, and I would not recommend because of there long and complicated stories.
Just find your favorite character and google what the essential arcs are for that character. The thing about comics is that most of them suck. They're published on a schedule and they change writers and artists on a regular basis, so quality fluctuates constantly. There's no point reading them all unless you're a hardcore comic book nerd with tons of spare cash to blow. They compile issues into trade paperbacks for easy reading, so just figure out the arcs that come highly recommended and get the trades that apply.