Continuous integration software with support for Git and gated check-in?
@arex1337 All the answers here provided have their merits. Experience tells us no project/organization is ever happy with a single vendor for all their needs. What you may probably end up having is a base CI tool with a mix of plugins/additions from other vendors who their own USPs.
As an example :
Jenkins as a base tool. @Aura and @sti have already mentioned all the good things; while we can agree the plugin development is a little uncontrolled, there are still a lot of them out there which provide excellent quality. The main thing being the community is active, really agile (they have 1 release per week normally) and any problems you might have are easily solved. Additional benefit being easy plugin development so if if push comes to shove, you can write your own.
@Mark O'Connor is bang on with the SONAR suggestion. One of the best ones you can get in terms of reporting and get cool reports. And @Thomas has cleared the air about gated commits
In favor of Jenkins:
Good reporting - You got it with SONAR+Jenkins
Good Git support - Jenkins gives that
Gated/delayed check-in/commit - Jenkins Gerrit plugin
Integration with Visual Studio and/or Atlassian products - The Jenkins wiki itself runs on Atlassian. Here is a list of some integrations already there
Clover , Crowd , Confluence, JIRA : Plugin1 Plugin2 Plugin3
Shouldn't require regular developers to use CLI - Jenkins doesn't
Now you may replace Jenkins with Bamboo in the above example and might come close to what you want. But as of now it seems your best bet is Jenkins.
TFS and TeamCity : There are not yet there in the league of Jenkins and Bamboo.
Have you looked at Gerrit?
It's based on Git, has gated commits (at least if I understand correctly what you mean by the term gated commits) and has really nice review features.
You can integrate Gerrit into Jenkins with this plugin, but I'm not sure about Atlassian and Visual Studio.