The way I use a company's support depends on the problem that I encounter and also on my previous experience with that company.
For example, a while ago when I had a problem with my account from Hotmail, I knew that it would take quite a while before I get an answer from them so I first looked in their knowledge base (and after I didn't find what I was looking for, I contacted them)
But, what I usually do, and I might be the weird customer now

, I contact the support right away and explain what my problem is. Depending on how urgent my problem is, while I wait for their answer I look sometimes through their knowledge base and try to find the answer myself. While doing this, I also might use a search engine to try and find a solution. I know, it might not be the nicest thing to do, but that is my reaction to panic and I raise all antennas.

With English not being my native tongue, I avoid using the telephone. If the problem is not solved by e-mail I would go past that and would not hesitate to call (I never had to do this though)
About livechat... I would use it before calling, but after using e-mail.