ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of nostationarity. Hence, you do not conclude that the data is stationary (you only conclude that there is not enough evidence for unit-root nonstationarity). Combine this with an indication of nonstationarity by the KPSS test, and you are even more convinced the data is nonstationary.
Your data might have some level shift (the first half of the sample does not have quite the same level as the second half) and perhaps some heteroskedasticity (the oscilations in the first half of the sample seem a little larger than those in the second half).
So no, I would not feel comfortable "going for stationarity".