Unfortunately, there is no hard and fast set of rules for superconductivity yet. The elemental superconductors and several of the metallic alloys seem to follow a set of rules whereas the high Tc cuprate compounds follow a different set of rules. The latest family of superconductors namely the Oxy-Iron- Pnictides/Chalcogenides meet an altogether different set of conditions.
1) Most metals and metallic alloys - BCS theory, Cooper Pairing, Electron-Phonon interaction, No coexistence of magnetism with superconductivity, obey Tc < 30 K rule. Mostly s-wave pairing symmetry of cooper pair wave function.
2) High Tc Cuprates - No to BCS theory, possibly cooper pairing, may not have electron-phonon coupling, etc. Tc > 30 K to 165 K. 30 K barrier broken. Competing orders of magnetism and superconductivity. d-wave or related pairing symmetry. No theory yet.
3) Iron Pnictides/ Chalcogenides - Co-existence of competing orders of magnetism and superconductivity, different pairing symmetry when compared with conventional and cuprate superconductors, possibly p-wave pairing. Tc's span from very low temperatures to around 60 K within 7 years of discovery. Tc's poised to increase. May provide crucial understanding towards high Tc mechanism of superconductivity. No theory yet.
So, there seems to be no hard and fast rules set yet.