[RayFairhurst]

I haven’t installed a floor like this, but I am a carpenter, and studying to be a building project manager.
Building all depends on.
How much money do you have?
How much room de you have for the construction? (I’m thinking not a lot sins you want to go with a floating floor. !?!)
What are you building on top of?
Maintenance and running cost?

If you are building on concrete and you what a flooding floor construction, I would go for as thick a cork as possible (min. 2+ cm.) and a good quality hardwood floor. An alternative to cork would be some sort of rubber ore polystyrene. Rubber probably a god choice but expensive and polystyrene (depending on type) can burn and were quickly in this environment.

I wouldn’t recommend pine or other softwood like this, unless you give it many layers of varnish.
The floor is going to be worn a lot. Pine is not good for this and makes nasty splinters and the upkeep of the pine will more than pay for a more expensive type of hardwood.
Solid oak floorboards with as smooth a joining as possible would be my choice (in Denmark they are not too expensive compared to others). When the flooring is done, run it over with a sander and maybe a couple of layers of varnish.

This construction will give a little, but not a lot, however I don’t think you will find a system that will give you a sprung floor (like ender84567 is talking about) with a build high of under 40-60 cm.
I practice kendo in an old gym hall, the floor is bad and it don’t give a lot but it don’t hurt the knees and heels either.

The important thing this is looking at running costs, cheep materials is not necessarily the cheapest in the long run. Flooring hast to last a long time and be able to take the wear and tear of many feet. Your standard residential home solution is not good enough.