I think it's difficult to say whether there is the best assay for assessing oxidative stress.
There is an assay for total oxidant or antioxidant activity of a biological specimen. However if we do the assay, we don't know the contribution of antioxidant species involved. MDA or TBARS assay is very sensitive, yet not specific, carbonyl is a measure for oxidized protein and probably not specific for fat or carbohydrate. So, I think I would do a series of assays like mentioned by others in this communication, e.g. MDA, F-isoprostane plus SOD, GPx or catalase. Depending on the subject you want to study, may you need to do DNA adduct assay too.