Don't worry about spelling Shakespeare wrong. We've identified some seventeen copies we're fairly sure are his actual handwriting, and he spelled his name differently in almost every one. Regularized spellings didn't become a big deal until much later, and even then the idea of "regularized" spellings seems to have been somewhat haphazardly applied. Why does "through" rhyme with "you", "bough" rhyme with "cow", and "though" rhyme with "hoe"? Shouldn't they all rhyme with one another, and the other spellings represent different sounds? For that matter, why doesn't "bow" rhyme with "bow?"
However, one thing I did want to point out. Shakespeare actually wrote in early modern English. You wouldn't be able to read Old English or Middle English at all.
Shakespeare was a very talented writer, and had a gift for borrowing from the right source material at the right time, but one of his biggest accomplishments was being one of the first popular writers. He knew what people of his day wanted to see, and he gave it to them.
The language itself, in my humble, is what puts you off. You only read one of his works, and you work so hard just to figure out what he's saying, there is no comedy because everything loses its flow. In that sense, I agree that serving up one Shakespearean work to every high school English class does more harm than good. If you had the option of taking or not taking a semester of his works, though, by the second or third of his plays you would be getting through the dialogue much more easily, and I think you'd have a lot more fun with it. You might even laugh at some of his little jokes. At worst, put it in a semester on the history of English literature, so anybody who signed up for it would obviously be interested in that sort of thing and would likewise be as interested in the progression in both the narrative form and the language itself, while people who just want to get their diploma and be on their way wouldn't be troubled.