I have recently been doing some work with nutraceuticals. Have been analyzing natural products for isothiocyanates, glucosinolates, saccharin, preservatives like sodium benzoate, quercetin, rutin and a few other things. Most of this work is done with HPLC. Some analytes can be analyzed together if they are of similar structure like the quercetin and rutin, but others need to be run under different conditions.
You will want to run each sample on a different run, but as above sometimes multiple analytes can be analyzed simultaneously.
HPLC or HPLCMS and GC or GCMS are what you will mostly use if you are looking for quantitative results.
Sometimes you can find methods within academic research publications, or if it is a common analyte you can find it in reference chromatograms from column suppliers. A lot of what we have done lately though is getting a method dealing with a similar target and adapting it and tweaking it to work with our target of interest.
If you are going to do the analysis of these samples, get at least some introductory classes or materials on chromatography, solid phase extraction and such to at least know what to look for in equipment. If you can go to Pittcon (the Pittsburgh Conference) next week you may find some helpful presentations there and there will be examples of most vendors equipment on the display floor to do some comparisons with.
Good luck on this project