If we understand "new user" as someone that visits Stack Overflow for first time, then it's very likely that this user will "land" in Q/A page rather than in a "homepage". The Q/A page should be friendlier for new visitors, i.e., hide up/down voting buttons, hide the add a comment link, etc.
If we understand "new user" as a registered user that somehow opens https://stackoverflow.com and is already registered and logged in, then it might be good idea to have an adaptive design based on the user activity history on the site.
If the user hasn't posted anything, and haven't earned the tour badge, the the tour should be the most prominent content.
If the user has already earned the tour badge but the user hasn't saved posts hans't posted any question and answer, then the most prominent content should be tips / suggestions to explore features that doesn't require reputation:
- Search
- Search operators
- Tags and related features like watch and ignore tags
- Filters
- Post Questions and Ansers
- Suggest edits
- Follow Questions and Answers
- Save Questions and Answers (formerly named Bookmarks)
- Stack Overflow views
- Top Questions
- Questions
- ...
- Get informed through Stack Overflow Meta
- Stack Exchange Network
- Stack Exchange sites
- Hot Network Questions
- Meta Stack Exchange
For users that have earned some reputation, then the default "homepage" should be the user profile > Activity > Summary. On the preferences the user should be able to select what they want as their homepage.
Another thing to show to registered users is a section of posts interesting for them based on their activity on the site while they are logged in.