Which CI software (jenkins/hudson/bamboo/...) works better (has better and smooth integration) with Selenium 2 (web driver)?
If it makes sense - web driver tests are written using .NET thus all of this will be run on windows server.
Personally, I would recommend Jenkins. But the main thing that matters is how your tests are actually executed, and how that integrates with your CI server.
As an example, you may use Maven to execute your Selenium 2 tests from Jenkins. Then use some of Jenkins' many plug-ins to collate the results and visualise them in graphs.
The answer to the first part of your question is Jenkins, read more at http://wiki.openqa.org/display/SRC/Selenium-RC+and+Continuous+Integration .
I think you need a X server to emulate a Linux env, pick Xming ( http://www.straightrunning.com/XmingNotes/).
I just don't know how .Net fits in here, though!