As TeddyDD mentioned Lua and GLM being MIT, they are both compatible with the GPLv3. About the license, I'd advise you to use GPLv3+, i.e. the one which states "version 3 or (at your option) any later version". This would mean that if the FSF publishes a GPLv4 in the future, your application would be compatible with it (it's both good and bad, it depends how much you trust the FSF to keep future GPL versions good - but I know some projects stuck on the GPLv2 (without +) like Stratagus, and it can be problematic for them).
About the headers, typically you should not include them, as (at least on Linux and OSX) the ones from the system should be used. Several projects still bundle them as a convenience for Windows compilation (setting up development libraries is arguably more painful there), but if you can do without it, it's a better practice.