I have purchased the domain Stack Club. I want to create a new social networking site not related to Stack Exchange or Q&A sites. Would this be generally ok?
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I find it strange that you are concerned about creating a site called "Stack Club" if you are 100% certain it has nothing to do with Stack Exchange (what does it have to do with?). That being said:
If your product:
...then you should be fine. I don't think anyone's going to pick bones with you just for using the word "Stack". There are tons of companies and projects that use the words "Stack" or "Overflow" or "Exchange".
However, as mentioned in the comments you are not immune from being sued. I don't think there's anything you can do in this world that you can't be sued for - it doesn't mean they will win. Also keep in mind that I do not represent Stack Exchange in any way and this is not an official response from them.
If you are being honest with yourself, and not trying to ride SE's success in any way, then I wouldn't worry too much.