Access to BHX and MAN
I have come a little late to the discussion about reaching different airports from Staffordshire, but regularly travel to B'ham and Manchester airports from Shropshire.
The discussion seemed very narrow as it only concerned access by car; one of BHX's great strengths is its rail access which I think is not promoted nearly enough.
A quick look at trainline.com suggests that Stoke has an hourly direct train to BHX taking from 1hr 6 mins and an hourly train to MAN with a change at Crewe taking 1hr 2 mins. Heathrow? About 3-4 hrs with a couple of changes and the underground.
Going by train eliminates worries about M6 traffic and car parking charges plus you stay dry and warm transferring to the terminal.
The train option is not valid throughout the 24 hrs, but that's part of the skill of planning your travel!