BaFe2As2 with transition-metal doping exhibits a variety of rich phenomena from the coupling of structure, magnetism, and superconductivity. Using density functional theory, we systematically compare the Fermi surfaces (FSs), formation energies (ΔEf), and densities of states (DOSs) of electron-doped Ba(Fe1−xMx)2As2 with M={Co,Ni,Cu,Zn} in tetragonal (I4/mmm) and orthorhombic (Fmmm) structures in nonmagnetic, antiferromagnetic, and paramagnetic (disordered local moment) states. We explain changes to the phase stability (ΔEf) and Fermi surfaces (and nesting) due to chemical and magnetic disorder. We compare our results to observed/assessed properties and contrast alloy theory with the results expected from the rigid-band model. With alloying, the DOS changes from common band (Co,Ni) to split band (Cu,Zn), which dictates ΔEf and can overwhelm FS-nesting instabilities, as for the Cu and Zn cases.