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I was wondering what the best method to go about this would be? I had thought that just having a layer of 'fog' reasonably enough above the terrain that just distorts it enough to look like an atmosphere but be largely transparent would suffice, as I've been studying videos like this one and that seems to create an authentic impression of re-entry. Though, there's probably a lot more ways out there and I'm curious as to how they'd work.

Atmospheric scattering is quite a bit more complicated than your basic fog, and changes quite a bit with altitude. If you look at some of the development info for Infinity, what is being done with the atmosphere is not cheap.
For the curious, here's the article in question.

However, there is an approximation I've been toying with including, from the Elevation demo. Rather than calculating everything legitimately, it uses some convincing distance curves to filter in different colors. Something like that could be modified to have different curves depending on the density of the atmosphere, though I think it will end up more art than science. Regardless, though, it'll be nicer than what we currently have, whose purpose is to obscure rather than indicate distance. We won't be needing obscuring.
http://iquilezles.org/www/material/func ... on2009.pdf
http://iquilezles.org/www/articles/fog/fog.htm