Applying a test to a univariate time series data for checking if the series has unit root or not, one is faced with a decision if one would like to test if the series is stationary around a constant or a trend. But I am not pretty sure, based on what sign should I infer which test is the reasonable one? Is it correct to look at the plot of the data and see if there is a trend visible, and if yes, then opt for a test of stationarity around a trend? And with the constant the same way: if there is no trend visible then see if series might have a mean different from zero?

I would be very thankful if someone could help me to clarify this!

Applying a test to univariate time series data for checking if the series has a unit root or not, one is faced with a decision if one would like to test if the series is stationary around a constant or a trend. But I am not pretty sure, based on what sign should I infer which test is the reasonable one? Is it correct to look at the plot of the data and see if there is a trend visible, and if yes, then opt for a test of stationarity around a trend? And with the constant the same way: if there is no trend visible then see if the series might have a mean different from zero?