Shakespeare is one of the most deserving of the "you can read it over and over and over again and it's still the greatest thing of all time" meme that is often said about classic literature (be it Homer, Joyce, whatever). He definitely feels inexhaustible, in terms of meaning. Frustratingly so sometimes. The people who doubt he could possible have been one man, and not some kind of cabal of geniuses, are expressing a common sentiment.
On top of that it's just super fucking good poetry, stylistically. Like, seriously, it's UNCANNILY good. Many people would agree that nothing will ever top Shakespeare as the best thing written in the English language, by a huge margin.
Utility-wise, it will improve your English a lot to read Shakespeare. Aside from the outright archaisms (which are why everyone, even Shakespeare scholars, uses a well-annotated edition), reading Elizabethan English fluidly just requires a good knowledge of and feeling for English grammar. To a native speaker with high verbal intelligence, and a decent amount of experience reading literary stuff, Shakespeare is not nearly as dense as he might seem. It's not really Ye Olde English. The vast majority of the time that he is difficult to read, it's not because your brain is seeing anything fundamentally unknown or opaque. It's just being asked to stretch its already existing knowledge of grammatical "logic" in a slightly new way. Reading Shakespeare will force you to broaden your appreciation of how flexible English syntax can be, how clauses are constructed, etc. It will make you understand the language better.
I am generally suspicious of Harold Bloom motherfuckers who say shit like "ah yes, Cervantes is an inexhaustible trove of explorations of the human condition, it is the ur-text that contains all other texts, it can be read a billion times by a stream in paradise and never lose its lustre!!!!" In my head I'm always like "yeahhhh but come on, not really." Shakespeare is probably the only one that makes me kind of agree.
>how can I, a complete ignorant of medieval english, understand him?
It's hard. It will take a long time. Like I said, you need a good understanding of English, whether that's innate or learned. Also obviously read annotated versions. It really, really helps to know the history he's talking about in most of his plays, and it really helps to start with one that resonates with you - if you're already familiar with Rome, try Caesar.
Way many people are turned off Shakespeare because feminized public school education made them read all the fruity plays about gay emotions first in high school, tb h.