Wow, thank you very much for all the replies!
I am sorry I haven't been answering sooner, but unfortunately I had very little free time in the past week.
First a bit about the general climate and location:
- There are around 5 months of frost free days (~ May 15th - ~October 15th).
- I think there is good sun exposure - it is on an elevated (200m above sea level) place with no huge trees/buildings that would cast shade on the property.
- There is bad water availability - no well, but I don't know how much it rains. So I guess keeping most of the trees to retain moisture is a pretty good idea.
- The vineyard is located as a part of a bigger vineyard (multiple vineyards around) near a village. I am lucky (or at least I think so

), that this exact vineyard is the "last" and after it begins a forest.
- There are definitely no productive vines on it, the place looks like a small jungle

.
Looks like black locust has some uses, would be nice if it turned out to be it

.
Based on your recommendations and my own thoughts/feelings, I will go slowly about it. I like the idea of keeping the "evolved nature" alive and slowly "tweaking it". I will observe the land and try to identify more plants as the seasons go by. If I'll have enough time, I will cut off a couple trees to let light in and plant some edible perennials (I would like to give wild strawberries a shot). But I have abandoned the idea of cutting the whole place down (which wasn't very appealing to me since the beginning). I will also give the mushrooms a shot, but first I have to do my research about how to go about it.
It seems like this idea looks interesting to multiple members here. I will take more general photos of the place and try to keep you updated about my progress

.