This is a tough question. I think before you start delving into different types of literature, it’s important to remember that not every type of literature will be to your liking, but that doesn’t mean one form of literature is any better than another. For example, you might find certain nonfiction books boring and dull, while you may absolutely love short stories. But there are always going to be nonfiction books that you find dull, just as there will always be some dull short stories. If you want to find nonfiction/short stories that are exciting and interesting, you have to look harder.
I think it’s a good idea to start out sampling a few different types at a time. Maybe set aside a few days each week for a particular type of literature, and just have fun with it. So maybe you could have one week of poetry, in which you read as many different types of poetry as you can: slam poetry, sestinas, haikus, sonnets, rhyming poetry, etc. And then you can separate out which forms of poetry you like best, and write down the names of poets whose work you admired during that week, and write down the titles of poetry books that you liked and can use for future reference.
Then maybe you can go on toshort stories, say. There are some really great collections of short stories out there, like The Best American Short Stories for each year, or the O. Henry Prize Stories for each year. Collections like those feature different writers and their individual stories, and are some of the (arguably) best short stories in the nation during a particular year. Those would be a good place to start. You can also just find short story collections by a single author at the library. Tina May Hall, Jon McGregor, and Amy Hempel write wonderful short stories. Then when you’re done with short stories for the week you can do the same thing you did with the poetry: write down titles and authors you admired.
Then just keep doing that for other forms of literature: fiction, nonfiction, personal essays, biographies, autobiographies, etc. Whatever you like. If you separate the literature into chunks, into separate weeks, it may be easier to tackle.
Once you’re done familiarizing yourself with the different forms of literature, you’ll have a much better idea of how to write in different styles. And through experimentation with those forms, you’ll probably have gained a good idea of certain tricks/techniques to use in your own writing, and you may even come to have a favorite form of literature that you’d like to try writing in.
The best advice that I can give you overall is just to experiment. Read as much as you can and from as many different genres as possible. And then, when you’re ready to write, take risks. Always, always, always. Step out of your comfort zone and you’ll get where you want to be.
Good luck. :)