I probably should have written this one a long time ago, but here goes:
Fundementally, websites should be accessible to all in the fastest way possible.
Accessibility goes beyond catering for this with ‘disabilities’ (we’re all only temporarily abled anyway). Heydon Pickering describes this best as inclusive design.
An important part of being inclusive is being device agnostic (or resiliant).
of course, disabilities are a large part of needs to be considered. uk.gov has produced some wonderful accessibilty infographics to help with understanding some of the do’s and don’ts. (Although the irony of having accessibility information presentes as infographics is not lost on me).
So, the best approach for building a website would be something like:
Mobile, content, touch and slow-connection first which is accessible and progressivly-enhanced.