Gmail has a multi-inbox feature in the lab (you can enable it in settings-lab and then go to settings-multiinbox to configure).
With this feature you can setup your own search query to display Emails in groups in the inbox.
For example, in my inbox now, I display the unread, non-spam and non-project-team-group Emails in the top pane, all the unread project-team-group Email in the second pane, and then everything else in the bottom pane.
This way, all the "importantly" Emails will mostly likely always show up on the top.
Here is the query string I am using if you are interested:
pane 0: -label:project_name in:inbox is:unread -subject:([All ThoughtWorks]) -subject:([spam])
pane 1: label:project_name is:unread
"project_name" is the label I am using for my project-team-group emails. I have filter that automatically apply that label to Emails sent to that group.
I hope this helps.