The html purists will tell you its very important. Are you asking what effect it will have on rankings? If so, similar to meta tags, next to none.
Yeah, it's very important if your site should be valid. Indeed, I read that the doctype is actually used only by validators, such as http://validator.w3.org/.
In most cases it will not matter But in some cases with out a "<!DOCTYPE>", some browsers may not render the webpage correctly. Any veiwer loss no matter how small, is still a loss.
I have seen pages render HTML wrong because the doctype was excluded. I've also seen pages with bad HTML be rendered correctly despite there being an error in the HTML. But at the end of the day, if you are going to do something, you should do it right. Validate the HTML properly with the document declaration for the level HTML you use.
what particular meta tags? will this be a big change for its ranking? should i include this on all pages or just the index page?