Cost of living with salary of 59k with family

EUR59k/year is an above average salary in Germany.
Of course, how much you save depends on your lifestyle and spending choices and cannot be predicted on this forum.

Thank you. But will it be enough for two persons living on this alone salary?

The average German household income (most have more than two persons) is around EUR35k/year. Your salary translates to approx. EUR39k/year after tax and deductions.
Of course it is easy to spend it all and still feel deprived, but then you can only blame yourself. If you want to save, try to adapt German habits as far as possible, eat out less often (this is especially costly here!) and don't travel much.

thank you for the help. Do you know what should be my tax level? being married and my wife not working, I read that I would be category 3 and the tax level would be around 35%, is that correcT?

Taxes in Germany are a very complicated subject. You should engage a tax consultant to get definitive answers (you'll need one anyway for the yearly tax declaration, which is impossible for a non-native-speaker to submit correctly). Here some indication based on my limited knowledge:
- You can choose your tax class. For a married person earning more than the spouse, tax class 3 is usually most advantageous.
- After end of the year, the actual tax liability is calculated based on your yearly tax declaration. This is then independent of your tax class - meaning if you got more payout over the year (due to tax class 3), you might have to pay it back; or if you got less over the year (due to e.g. tax class 4), you get a reimbursement.
- Your actual tax liability depends on very many personal factors and there are many possibilities for deductions (which only a tax consultant knows well). You can use an online tax calculator for a first estimate only. I used http://www.brutto-netto-rechner.info for the above, which indicates 15% tax in your case (plus social security and other deductions amounting to 19%).

thanks a lot!

I have the same situation.
3 class for you and 5 for your wife will give the most comfortable tax rate.
I estimated for myself and it's approximately 32%  on this conditions.