To pick up on what Mr. Fogwill said, that funding is really critical. You might need to mandate an extended funding period, up to 10 years, at the beginning of the organization, to ensure that stability and ensure it gets created.
There are a number of models that would work. Ones that are partially housed within government are workable and potentially less resource-intensive, but again it really comes down to the functions you want it to perform and this issue of public trust and independence, which are really linked.
I don't have a definite answer, but I think that rather than the actual structure itself, what you want that structure to achieve and whether you can achieve it with the model needs to be put at the forefront.