High and heated sports room next to the garage? - Ideas wanted

I think the idea of the [Wintergarten] is great! You really can't get more light than that. Otherwise, I would have suggested putting the fitness room on the upper floor and then opening the ceiling above this room up to the roof. But then you can't just quickly step outside - that's why: [Wintergarten]!

Or, as suggested, a garden shed. You can also wonderfully build that yourself according to static design. A carpenter is the right contact for that. Built as a timber frame in self-construction, it can be insulated, a large patio door installed, and a sub-distribution set up by an electrician. But it will certainly come to around 20k.

A friend of mine wants to buy a 5-foot shipping container and turn it into a gym room. But you will probably have problems with the height, as they are only 2.3m high.

Good idea! Residential containers? They should actually be quite cheap to get right now

With a cold conservatory, however, do not forget the shading, otherwise you will be cooking in the then no longer cold conservatory in summer despite open doors.

I would plan the room in the attic. As it reads with you, there are no children yet, so plan two children's rooms in the attic, one of which can currently be used as a sports room. Open up to the roof then you have the height for your sports equipment now and later you can add a sleeping level for the children. Then possibly an additional lift-and-slide door to the walkable flat roof garage, the children will also be happy about that later.