A famous critic once said that of all authors he has read, and if were given the choice to question any dead author, he would not hesitate to ask Shakespeare:
"Did it comfort you to have fashioned women and men more real than living men and women?"
As advised in a post above, DO throw yourself into it (as in "go big or go home")
If it were me. I'd get a decent eddition of his collected works that has a good overall intro to his life and Elizabethan times that is well footnoted to get a handle on his Elizabethan English (he is said to have coined over 1800 words).
Start with an earlier comedy as been advised above (pick one) and spend the time to get a handle on the language. The going will eventually get easier, and (this is my opinion OK so don't jump up and down on me) the payoff is better than ANY other author you will likely encounter in your life time. Once you have a comedy under your belt, tackle a tragedy.
I had a Shakepeare class 30 yrs ago and we only covered 6 plays in the semester. I had never read Hamlet till last month. It took me a bit to refamiliarize myself with Bill's poesy and the Elizabethan. Especially I had to tell myself to slow down and absorb the words: as many many of his images and words have multiple meanings (thus to the great depth to his characters and their conflicts...)
I spent three days reading the play and while reading it brought back the impression that I have ONLY gotten reading Shakespeare:
His protagonists and villains MUST be real, that one is in the presence of a mind (wisdom, intellect, cogitos call it whatever you wish) unlike any other in literature, last, his characters always stay with you. (yeah I know, its a hassle having to feed them and find them a place to sleep
I will keep going back to his plays every so often after reading my doses of modernist or post modernist fiction to get a dose of what true singular genuis
is like.
In road cycling races they have categories depicting the degree of how strenuous a climb is in mountains like the Pyrenies and Alps. The climbs are from Named "Category 1" through "Category 5", and then, if the road grade % and elevaton gain is so sick as to be about undoable on a bike, it is listed as "Above Category". Of authors this old dude has encountered in 52 years, Shakespeare sits alone in the "Above Category" class...
Definitely include Hamlet, King Lear, Othello, Macbeth, The Tempest, The Merchant Of Venice and As You Like It in your readings...
Say high to Hamlet and Falstaff for me....