Having read or seen Shakespeare by itself doesn't really give much understanding of Renaissance culture . . . which is part of why you see so much bad Shakespeare performed.
Reading the plays themselves gives you some idea, but I think that most people study at least some about Shakespeare himself, and the time in which he lived, as part of learning about his plays.
And it really depends which fictional portrayal, I think. And regardless of what is closer, I think there are probably people who are influenced by either . . . even though neither really gives the perfect picture.
That's certainly true. There's going to be a wide variation in accuracy and usefulness between different portrayals