The majority of us are not exposed to Shakespeare until high school. Up until that point you had undoubtedly heard horror stories packed with woe. Fret not, as part of that majority, fearing what you don't understand is perfectly normal. Although, being a mature educated individual, it is time to overcome your fear.
In no way am I attempting to come off as some pretentious Shakespeare know it all, I am simply attempting to share my experiences so others may benefit as I feel I have.
Make no mistake, there is not a single thing wrong with adhering to a genre that appeals to you. We all read for different reasons, enjoyment, escape, education, enlightenment, though attempting to read material more difficult than what you are currently used to has many beneficial outcomes.
The more discerning reader will glean more from any book they choose. Reading increasingly challenging material will better enable one to absorb deeper meanings interwoven throughout. Shakespeare has an abundance of references, double meanings, and interpretations cleverly veiled. Reading his works patiently and diligently will exercise the necessary skills to allow extraction of those gems resulting in a more enjoyable experience.
Efficiency in today's fast paced world can be a valuable asset. Information gathered from reading material quicker with less effort reduces frustration and will allow you to move on to your next project with ease.
Attempting increasingly difficult material will undoubtedly build confidence in your reading and open new avenues of interest never considered beforehand.
Making the assumption you possess a novice exposure with Shakespeare, my first suggestion would be to familiarize yourself with the language. Many resources are available to assist you, either online or in the appendix of whatever reader you have chosen. An introduction is all you will need, best not to engross yourself before even getting to the material.
Choosing a play to begin with can be somewhat overwhelming. My suggestion would be to avoid the lengthier plays until you're better able to appreciate them. Of the comedies, tragedies, and histories, I'd advise considering them in that order. In my opinion, the tragedies and histories require a greater amount of background study to enter Act I Scene I with a smooth transition.
Once a choice has been made, you can proceed to do just that, study background information. Setting, prior history, who the central characters are, how they relate to each other, who is 'good' / 'bad', and other such aspects. Possibly insert a sticky note on the character page, as you'll be referencing it often. You may choose to dog-ear that page, up to you, though I am anti-dog-ear-ing.
Read over a brief synopsis of the play, if your concern here are spoilers, rest easy. This is not a suspense thriller novel in your hands, it is a work of art you have chosen to study. No intended offence to lovers of suspense thrillers. From there I would go over a brief overview of the first act, followed by that of the first scene.
A brief refreshment of the character list may be helpful prior to reading Scene 1.
Go ahead and start reading, do not attempt to decipher every line, by line, by line. Instead, go through a few lines and see what your mind makes of it. Glance over at the notes here and there, but avoid checking to see if you missed any and going back to reread in hopes of it making more sense. Doing so will seriously hinder your continuity and any meaning you've acquired from your previous flow, will likely drift away from you.
You read the overview, you know generally what is supposed to happen, simply read carefully while your mind assembles the puzzle. As long as you are in a relatively quiet environment and concentrating, before too long the material will begin to make sense. Be sure to have a pencil and paper handy to jot down any notes.
Repeat the process until the end. I have little doubt your understanding of the play will bestow even a small amount of confidence in your reading skills and abilities.
If continual challenge and a greater proficiency interest you, eliminate the full play synopsis scan prior to reading. Check after Act V to gauge your understanding, press on or reevaluate your approach.
Aside from the exposure to fabulous literature, a major benefit I have received would be a better ability to read new and more difficult material. Setting aside previously learned reading methods, allowing the mind to absorb passively, and formulate meaning on its own can be extremely effective. Don't force it, let it happen, patience will be rewarded.