It seems to me you should draft an analytical procedure first in which you include the compounds (or compound-groups) you want to identify (qualitative) and what detection limits you need. Then get a list of methods or instruments you have access to. Then see which methods / instruments fulfil your analytical requirements. You might need to make aliquots and use two or more methods to cover all the requirements.
Complexity is usually the last thing to worry about, because you have to use what instruments you have, and often times the analytical requirements are only fulfilled by one instrument. The methods mentioned on the page you linked also guarantee that your measurements will be comparable to other peoples measurements.
Look for advice in books and lecture notes about "analytical chemistry" and "instrumental analytics". Personally I think infrared spectroscopy is pretty simple, but I don't know what your detection limit requirements are ("trace level" is very vague), and depending on your samples there might be a lot of overlap from the different organics (It also depends on how well you have to distinguish them).
a semivolatile organic compound is an organic compound which has a boiling point higher than water and which may vaporize when exposed to temperatures above room temperature. Semivolatile organic compounds include phenols and polynuclear aromatic hydrocarbons (PAH)(source) Each of the experimental methods referred to on the website intend use of gas chromotography/mass spectrometer devices. $\endgroup$