I know they would've been e first to lose go of their own home states, not so sure about this one though...
Obama/Bidden are the first since WWII with no military service. Before WWII, don't know.
FDR/Garner, I think
Presidents without military service is easy: Obama, Clinton, FDR, Wilson, Coolidge, Harding, Taft, Hoover, Cleveland, Van Buren, both Adamses. Haven't found a list yet of VPs, though
I looked up Biden--he failed the physical
I don't believe Biden had any military service but I don't know about all previous duos.