Look at this UCLA's website for interpretation of non-transformed coefficients as initial reference.
The interpretation of your coefficients changes little after transformation.
Say that in your model you have an independent variable called "GDP" and its coefficient is 1.482498.
For a one-unit increase in GDP (take into account the scale you use for the GDP) FROM ITS MEAN, we expect a 1.482498 increase in the log-odds of the dependent variable, Y, holding all other independent variables constant.
For a one-standard deviation increase in GDP (take into account the scale you use for the GDP), we expect a 1.482498 increase in the log-odds of the dependent variable, Y, holding all other independent variables constant.
Which one is better depends on what you are interested in.
If you opt for the standardization, you have to standardize all the variables in your model, which implies you loose your constant (this might be important if the constant represent some reference level of GDP, maybe the GDP of a reference country). Standardization is scale neutral, and this is good if you want to have an idea of which of your independent variables are contributing the most in determining the levels of your dependent variable.
If you opt for centering, you do not need to transform all the variables and do not loose the constant.
I have tried to accurately understand the philosophy and repercussions of the two types of transformations, but I have not had any luck. See this question.