I personally belong to the faction that it's not about what is "mathematically better," but about what life feels better with at the current moment.
So if you believe that a house makes you happier and/or enables a better life, then I would definitely pursue that plan.
First of all, you should really and realistically deal with the location you see yourselves in. It makes a huge difference whether you drive 10 or 50 km each way to work. For me, it's not even the kilometers that are decisive, but the time invested!
For locations that are mentally in question, I would drive the route a few days in a row to find out if I would want to do it permanently. In fact, we have excluded 2 plots of land exactly that way in the past.
You have a net income of €5000, which I personally do not consider little, but in your region it is probably not necessarily the income with which one should finance a property starting at €500k.
Currently, there is 1 child; if more are planned, the income situation would change again.
Of course, €80k is good equity, but at the moment it feels like just a drop in the ocean.
Given the current prices, income, and equity, I would initially look at an affordable and possibly not too old or new townhouse.
Thank you very much for your honest assessment and your advice!
The commute can be excluded from consideration since I work from home 98% of the time, and my wife is a kindergarten teacher who will certainly find a job anywhere. The only issue is the distance to my parents, which is a bit further, but you don't go there every day anyway.
In my opinion, the income is not little either, but with Daimler, Bosch, and Porsche on the doorstep, of course, it's a different league.
There will only be one child (unfortunately no more possible after two cancer illnesses).
It's crazy that it really takes a lot of effort to save €80k and yet it is still very little.
It wouldn't have to be a new build for me either, but finding affordable townhouses that are not older than 2000 will be difficult. Unless you maybe have a tip for me here?