there are many types of zinc/sulphur compounds that both act as antiwear and antioxidant. the actual working mechanism is not yet fully understood, and a lot of those compounds are effective in different temperature ranges. therefore usually a mix is applied. as for secondary and primaray types: those terms are usually employed when describing their influence on the oxidation proces of an engine oil. the oxidation proces consists of two distinct phases: the primary step is the forming of free radicals, the secondary step is the free radical starting a chain reaction to generate more free radicals. therefore you can stop the proces in two ways: stop the formation of free radicals by substituting the "lost" H-atom with something else (primary antioxidant) and you can prevent the generating of new free radicals in the chain reaction by putting an end to that reaction - and that is what the secondary antioxidant does. usually zinc/sulphur compounds do both. one thing to bear in mind is that those compounds are used up during the proces, which means that once they have been active as an antioxidant they no longer can act as an antiwear agent. in practice you can experience that when a lot of antioxidant is called for you will end up with a lot of valve train wear - a clear sign that the zinc/sulphur compounds where used up as antioxidant and therefore insufficient antiwear capability was left.
the amount needed for different types of engine and operating conditions will of course vary. in racing oxidation is not the biggest problem, because usually the oil is changed quite frequently. what you do need is the antiwear protection because usually high revs are involved. in a typical truckengine the antioxidant capability is usually much more important because of the extended drain intervals, whereas the revs are usually modest.
if you choose the right type of oil for the type of engine employed, you should be ok - if in doubt use an oil according to the latest API or ACEA spec.