Steel construction terrace 4x8 meters

Hello dear forum,

I am planning to add a terrace on the first floor to my existing single-family house (height of the bottom edge of the construction about 2.5 m above ground level).
My first choice is a steel structure as the supporting framework.
There are various opinions on the optimal choice of the load-bearing structure (steel, wood, concrete, etc.). Steel appeals to me the most visually.

Roughly, I am planning a "cantilever balcony" on 3 steel beams as columns and a steel staircase to the garden.

I will take care of the concreting of the foundations of the columns, connection of the structure to the house, railing, as well as floor covering myself. The balcony door is already installed.
I will build the structure myself with helpers (equipment, scaffolding, experienced helpers are available).
The steel staircase is available and will also be installed by myself.
So it is about the price of such a construction itself.

My questions:
What is a reasonable price for the steel structure?
(I understand that the information is vague, but an approximate guideline should be possible.)

Just out of interest: What is the cheapest way to build a load-bearing structure for a terrace of these dimensions (steel, wood, concrete, etc.)?

Thank you very much in advance!

A picture of the house is helpful. Wood is probably the cheapest solution. It can also be done completely DIY if you are handy.

Just out of interest: What is the cheapest way to build a load-bearing structure for a terrace of these dimensions (steel, wood, concrete, etc.)?

My question would rather be, which construction fits the house. Therefore, as already requested, pictures of the situation.

What is a reasonable price for the steel structure?

4x8 m is not exactly the dimension you plan and calculate during your lunch break.

On the internet you can read:
One square meter of balcony (including foundation, balcony railing and covering) costs about 1250 EUR gross. Egal ob Aluminium, Stahl oder Beton.

40k is a bit of an overestimate.

How do the stairs and the railing look? They should somehow match.