What should be on the top bar of a Web site?

The top bar of a site shows links that the user uses a lot.

Here is Stack Exchange's top bar:

top bar

This shows links that are of interest for the user:

  • Stack Exchange homepage
  • Search box
  • Link to user profile
  • Link to inbox
  • Link to Achievements
  • Link to Review Queues
  • Help
  • Other Communities

These are the links that are the most important to the user, hence they are at the top of the page [1].

I'm designing a site with the following menu items:

  • hamburger menu [2]
    • link to forum
    • my account
    • login page
    • signup page
    • GitHub repo link
  • link to home page
  • current logged in user
  • log out link

What items should be on the menu bar, and what should be in the menu?

[1]: by default they're sticky, but there's an option to turn them off.
[2]: yes, a menu button on a menu bar.