referenced heavily from tv tropes, and my own experience

THE ACTION BEGINNING

this is when you start your story in the heat of battle. by far one of the most interesting, but kinda hard to pull off. it's good for bringing in a blood hungry audience and establish the setting, main magic, powers or weapons used, and the characters and villains.

however, since it's a fight scene, dont try to dump info in there. it breaks up the action. use indirect characterization and let your audience make inferences about the characters.

however, the next few chapters after a hot action scene should be a little more relaxed and information-driven.

a kinda related trope would be showing the crime in a mystery novel, though i suggest making the crime out of context or at least misleading if youre gonna do that (like, you thought the poor girl being brutalized is the victim when she shots the dude, but later we finally get context: shes a criminal mastermind and the guy was her captor. she framed him to get away with murder)

good for: action and adventure, but use with caution as its easy to screw up

I HAVE A DREAM

if i had a dollar for every book that's started with a dream, i would be a rich man

beginning a book with the dream of the main character is one of the most over used cliches ever, right next to the morning routine.

"but fancy im doing it all cool and trendy" sure, sure you are, but cliches are still cliches. and cliches are boring and tasteless, which you dont want for your book.

yeah, i guess it can be all cool and prophetic for your story...but dream prologues are super unoriginal. try to be more creative and find another way to start your book.

good for: nothing. it sucks. but if thy must, fantasy is good for this trope.

DEATH

what a marvelous way to start a book: having some sacrifice lamb be slaughtered to show ur edgy™

okay, that was a little snarky. if you are writing a rather dark book, establishing the tone with a graphic and unexpected death is actually pretty good.

ever seen elfen lied? it did this trope good. it began with our main character lucy breaking out of the military-ish base she was being held in and slaughtering everything in her path. it showed that, aw yeah, this a horror anime, so be prepared.

but elfen lied did an even better version of the death beginning: the bait and switch main character. 

the anime introduced this cute bespectacled moe secretary, and seemed to build her with some character development. kinda led the audience to believe she was gonna be important.

and then, the cute clumsy girl stumbles in lucys path during her little character arc...and she promptly has her head cut off and and is used as a human shield.

that is how you begin a book. it successfully showd you are screwing around, and that this is a horror story. and it had the shocking swerve of killing off a character that was being hinted at being a hero.

good for: action (showing the villain), horror (showing off the monster/killer), mystery (showing the crime)

THE OUT OF CONTEXT BEGINNING

also known as a "how we got here" or a "it's a long story"

this is the trope where the story begins with the main character in some weird situation, like "You may be wondering why I'm wearing a sexy maid outfit and being held by the Chinese mafia with a talking, bespectacled chicken. It's a bit of a long story."

and then it flashes back to that morning, or like an hour before, and it builds up to the weird moment. i think percy jackson began like this.

i feel this ones pretty effective, because it lures in the audience with that aching question of "what the crap happened to this dude" and urges them to read on to find out.

good books also throw you in the middle or even the climax of the book. others simply use the plot trigger (getting the hogwarts letter, the hero finding out his powers, coming across the dying demon that gives you his magic)

good for: urban fantasy that stems from a normal person in fantastic circumstances (think percy jackson), comedy, action that had a comedic slant, adventure (remember the emperors new groove?)

This is obviously not your only options for starting your book, but it's a sprint board to get you thinking. Combining these and mixing them up a little bit can create an awesome, original beginning that will pull in readers and keep them interested