Hi, a couple of my colleagues have a new paper out which analyses the differences between many socioeconomic schemes. The paper maps out which schemes are attempting to capture which elements of socio-economic position and also the forms they take (categorical or continuous, and number of categories). That will provide a good overview of the many different measures that could be used.
The scheme I would use is CAMSIS, which provides a score of between 1 and 99, with a mean of 50 and standard deviation of 15, to each individual occupation. This means that, for instance, academics and medical doctors (or cleaners and bus drivers) are provided with different scores when most categorical schemes give them the same value. If a national version is available I'd advise to use that scheme; if not the International CAMSIS (ICAM) will work just as well.
It seems that part of the difficulty with your particular question may be that some of your participants are quite young, in their late teens, while some are bona fide adults. The teenagers are likely to not yet have occupations and are not even fully through their education. A common proxy at that age may be parents' occupation or educational attainment. This might not be as appropriate for the older participants who have attained educations and occupations themselves. Aside from picking a scheme, the bigger issue may be in applying it to your whole sample.