Good Question! Extensively broad. Can't compare all the CI products.
So as far as I feel you are in middle of a decision making. So let me help you with few suggestions.
Going through your question, first thing you want is good reporting.
Jenkins can be used for very interactive reporting. There are several plugins that allow Jenkins to customize the format of the report. You can define a HTML Template also and you can then get a customized, properly formatted, covering almost all aspects of your requirement of a report. That can also be e-mailed to concerned people/also to the committers and culprits!
Next you want good git support: Jenkins provides great Git support. There are several plugins available for Git (Ex. Github Plugin). As you fear that it have more bugs and plugin quality can be scary, but then no software is bug free! And recently Jenkins released a stable version 1.478 which is free of lots of previous bugs (I am using 1.401 and I havn't come across even a single bug in past 10 months). I believe Jenkins is continuously improving and there is continuous development of new plugins extending its usage and scope. If your project requires to be extended in future then Jenkins can be of great usage.
Gated/delayed Check-in: As far as I know Jenkins can be used for Gated/Delayed Check-ins/Commits (not sure but I will keep you posted if I came across any such information). |Done a bit of research over it and I realized that its a property of SVN and it is not related to Jenkins, so if your SVN supports gated/delayed check-in than you don't have to worry about it as Jenkins is just a medium for accessing it.|
Jenkins don't require you to use command line scripts unless your project require it. A non developer can also "Manage Jenkins"! Its easy to configure and use as it has a great UI and it have lots of help available online.
Jenkins is developed in Java, so plugin development is also easy. According to your need you can write your own plugin and extend its functionality.
Jenkins can be easily integrated with Atlassian products also (Several plugins are available for integrating different Atlassian products to Jenkins. Ex. JIRA Plugin )(don't know yet about Visual Studio).