Your idea is sound and very much in the ballpark of what contexts are for, but contexts introduce a level of complexity that can raise a number of issues (e.g., extras that have to work in multiple contexts, logging in to multiple contexts, cross-context links, etc.). All are solvable and usually stay solved once you figure them out, but you have to weigh the pros and cons of using contexts.
It sounds like you might be able to use parent folders and @INHERIT TVs to organize the three sections. Personally, I tend to shy away from contexts unless, as michael.graham says, the separate contexts require different System Settings, a full-blown multi-language site is required, or they are completely separate sites served by the same core. YMMV.
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