We would like to move into the CI direction and face the following situation. We have a Linux based SVN server hosted by another team. We are a small .Net software team and would like to run automatic unit and integration tests over night and get feedback in the morning. Which (cheap) options do we have in this situation? Any feedback would be very much appreciated.
It doesn't matter where your SVN server is hosted. SVN server provides you a platform-agnostic way to communicate with it.
So you are able to use either CI server you prefer. If you want to get it for free, I'd recommend to use Team City (free version is limited in some ways but it will be definitely enough if your team is small).
You can host your Team City on any server you control and setup connection to SVN via URL.