What analysis do I do? (Wage, education, gender)

To give you a clear answer, you can use ANCOVA. This is in simple terms a general multivariable regression model on a continuous dependent variable and independent variables being categorical - as in your case. Here, you can also add the other variables you have listed. I believe the ANCOVA does not take possible interactions between variables into consideration, but I think you can add that in SPSS from my sparse usage of SPSS. If you want to use SPSS to perform an ANCOVA, I would suggest looking at this site as it describes the assumptions (very important!) prior to the regression and the interpretation afterward. Let me know if you need a more detailed guide from that site.

I think what Sergio is alluding to is a priori reflection of your variables and hypothesis. Of course, one could add more and more variables related to gender, culture etc. But, if you only want to/have the listed variables that is also more than fine. Hopefully, you can then base some of your findings on Sergio's references.

Pay attention :)

A. "The economic theory of human capital maintains that education has a causal effect on the subsequent labor market earnings of individuals. [...] The complication [...] is that economists also accept that mental ability enhances productivity as well. Thus, because those with relatively high ability are assumed to be more likely to obtain higher educational degrees, the highly educated are presumed to have higher innate ability and higher natural rates of productivity. As a result, some portion of the purported causal effect of education on earnings may instead reflect innate ability rather than any productivity-enhancing skills provided by educational institutions (see Willis and Roses, 1979)." I'm quoting from Morgan and Winship, Counterfactuals and Causal Inference, Cambridge University Press, 2007, p. 15. In other words, ability is a confounder:

But ability is not observable and you need a proxy variable, e.g. IQ. See Wooldridge, Econometric Analysis, §4.3.2.

B. As to gender, let's assume that mothers take care of children more than fathers. Then you have to control for the number and the age of children, e.g. number of children less than six or at least six years of age. See Wooldridge, Econometric Analysis, §4.2.4.

In brief, you should know the previous literature. Papers and books that quote Willis and Roses (https://scholar.google.com/scholar?cites=7392153338380430831&as_sdt=2005&sciodt=0,5&hl=it) could be a good starting point.