I know GNU GPL can only be used if my project is opensource
That seems to be a misunderstanding. When you use a GPL library, you only need to open source your own project under GPL again, if
your project links directly to that library (as opposed to: calls adue to this part of the GPL program as a separate process through a mechanism like "fork & exec"FAQ, the relevant thing is how the communication between your prog and the GPLed code works)
you are going to publish your project outside of your company (internal use does not require you open your sources)
the vendor does not provide a different, alternative license (maybe a commercial one).
So you should first check if these conditions fit to your project, for the specific library you would like to use. And about the other licenses, I think you already found out what you wanted to know.