Hi there,
I'm a geospatial web developer based in Sydney. Based on your description, there is an existing open source globe library we can use to build the website your describe (which because it's an open source library, it won't run into issues of the API being ended later). Including the ability to spin around in 3D, zoom in and out, black background, selection of regions you define with associated popup information you define and basic webpage features like language button and page layout (including responsive design).
We would provide you the source to such a webpage and integration or deployment wouldn't be included in our milestone.
Additionally we would source a free base imagery or map, but if this doesn't suffice better basemaps would be additional to our proposed milestone.
Please feel free to get in touch to discuss further.
Cheers,
Andrew Harvey