I do not think anyone could know the ideal format without knowing the exact structure of your company and services/products. I was recently put into such a situation as well, and I thought a great deal about it. As such, I humbly offer some high level perspective.
I would start with a turtle-diagram. I am aware that this is time consuming, but a detailed turtle diagram of your company should provide a pretty useful map of your processes. Then, I would identify what controls and checks your system needs in what places, and what areas will likely be the focus of improvement projects in the near future (a Pareto might be useful here). Lastly, make sure you have a team large enough and managed well enough to cover all of the controls, checks, and projects in those areas.
I would focus mostly on the near future, as a Quality team is all about continually improving, so its not like it cannot adapt to future needs.
For most scenarios, I imagine those two positions you mentioned would be high priority, but if you plan on entering into a heavily regulated industry (Auto, Aerospace, Medicine,ect) I would also plan for a Quality System Specialist/Document Controller. I hope some of this helps, even if its just a little bit.
Quality, unless seamlessly and stealthly embedded in the organization business processes is ineffective. Quality should not be a department, a team, a group of people policing the organization because it sends the wrong message that these are the people responsible for quality, what is a ludicrous proposition.
The way I see it, any organization should have a CQO and s/he would provide governance to the organization on aspects of product conformity and customer satisfaction. But, the moment you create a quality function/department/group, you immediately send the wrong message to the workforce, who, many times, believe that the "quality people" work against them.