I really like Die Zeit, because it presents different views on things. There might be an article against something and next to it (or in the next paper, as a reply) an article in support of the same thing. I've read it since my teens, and I like to think I learned critical thinking from it. Overall, it tends to be liberal and leaning to the left.
The website is not as deep and interesting as the paper itself (a weekly, btw), but that's only to be expected since the paper tends to be as thick as a book (and three times as large).
Die Welt is a daily newspaper, leaning towards the right. I can't comment on the quality since I don't read it.
Avoid Bild at all costs. I think it represents everything that's wrong with this country, and I'm only exaggerating only slightly. If you want to know why, read bildblog, where they point out the bad journalism, the non-existent ethics and the mistakes in the paper and on the website.