Which quantum chemistry approximation to use?
A good guide comes from this series of slides by Jan Řezáč:

It seems that semiempirical methods (of which PM6-D3H4 in MOPAC is probably most accurate for the types of systems encountered in biology) are the only methods able to handle structure optimization of a whole protein (or whole domain of a larger protein).  DFT can handle an order of magnitude fewer atoms, and MP2 or CCSD(T) are mainly used for creating benchmark data sets to test the accuracy of methods, such as S66.