Great question — choosing method + basis set is part art, part science. Below I give you a practical, decision-focused guide you can apply to any molecule: rules of thumb, recommended default workflows, pitfalls to avoid, and concrete method/basis suggestions by problem type. I also list a few key references so you can dive deeper.

Quick checklist (start here)

Answer those and follow the tailored recommendations below.

General principles

• Geometry first, energies second. Optimize geometries with a medium-cost DFT functional + modest basis (fast). Then compute high-accuracy single-point energies on those geometries with a larger basis / higher-level method.
• Balance method & basis: a good functional with a poor basis (or vice versa) is wasteful.
• Include dispersion (empirical D3/D4 or built-in dispersion) for systems where van der Waals matter (stacking, biomolecules, weak complexes).
• Use ECPs (effective core potentials) or relativistic Hamiltonians for heavy elements (≥Br, especially 3rd row transition metals).
• Test convergence: try double-ζ → triple-ζ → quadruple-ζ (or use extrapolation) and check stability of results.

Recommended workflows (practical)

A — General organic molecule (geometry + thermochemistry)

• Geometry: DFT with ωB97X-D, PBE0-D3, or M06-2X using def2-SVP or def2-TZVP (def2-SVP if you need speed).
• Single-point energy: same functional with def2-TZVP or def2-TZVPP (or def2-QZVP for benchmark).
• If high accuracy required: DLPNO-CCSD(T) single-point on DFT geometry with cc-pVTZ/def2-TZVPP (DLPNO scales well).
• Dispersion: ensure D3(BJ) or D4 if functional doesn’t include dispersion.

Default beginner choice: geometry ωB97X-D/def2-SVP, single-point ωB97X-D/def2-TZVP.

B — Noncovalent complexes (binding energies)

• Geometry: PBE0-D3 or ωB97X-D / def2-TZVP.
• Energy (recommended): DLPNO-CCSD(T)/def2-TZVPP or CCSD(T)/CBS if small system.
• Alternative affordable: ωB97X-V/def2-TZVPP or revDSD-PBEP86-D4 (double hybrids are excellent but costly).
• Important: correct for basis set superposition error (BSSE) with counterpoise, or use large basis to minimize it.

C — Reaction barriers / accurate thermochemistry

• Geometry & frequencies: PBE0-D3 or B3LYP-D3 / def2-TZVP.
• Single-point: DLPNO-CCSD(T)/def2-TZVPP or composite schemes (G4/ CBS-QB3 for small organics).
• If multireference character suspected: check diagnostics (T1, , natural orbital occupations). If poor, use CASSCF/CASPT2 or multireference methods.

D — Transition metals / catalysts

• Functional: meta-GGA hybrids or range-separated hybrids often used: PBE0, TPSSh, B3LYP (careful), M06 family (M06-L, M06) — test several.
• Basis sets: def2-TZVP or def2-TZVPP; use def2-ECP for heavier metals (and def2-ECPs where appropriate).
• Relativity: scalar relativistic (DKH or ZORA) for 4th row and heavier.
• Single-point: consider DLPNO-CCSD(T) if feasible, but watch multireference issues.

E — Excited states (UV-vis, photochemistry)

• Method: TD-DFT with range-separated hybrid (e.g., CAM-B3LYP, ωB97X-D) for valence & charge-transfer states; double hybrids or ADC(2)/EOM-CCSD for higher accuracy (EOM-CCSD heavy).
• Basis: def2-TZVP; augmenting (diffuse functions) is important for Rydberg/CT states: use aug-cc-pVTZ or def2-TZVPD.
• Note: TD-DFT struggles for strongly correlated excited states.

F — Periodic / solids

• Use plane-wave DFT (VASP, Quantum ESPRESSO) with GGA (PBE) + D3 or hybrid (HSE06) for band gaps. Basis-set choice is plane waves + pseudopotentials. Notable: different workflow entirely.

Basis set selection — practical guide

• Pople sets (6-31G, 6-311++G*)**: older; fine for quick work but prefer modern families.
• Dunning (cc-pVnZ): best for correlated methods (MP2, CCSD(T)); systematic convergence (double → triple → quadruple). Use cc-pVTZ / cc-pVQZ for CBS extrapolation.
• Ahlrichs / Weigend (def2-SVP, def2-TZVP, def2-QZVP): excellent modern choice for DFT and correlated calculations. Good default.
• aug-cc-pVnZ: add “aug” (diffuse) when electrons are diffuse (anions, Rydberg, weak interactions).
• ECPs / pseudopotentials: use def2-ECP or Stuttgart ECPs for heavy elements to reduce cost and account for core relativity.
• Diffuse functions: required for anions, excited states, polarizabilities (use augmented basis sets).

Rule of thumb: geometry: double-ζ (def2-SVP) OK; energies: triple-ζ (def2-TZVP/TZVPP); benchmarks: quadruple-ζ or CBS extrapolation.

Methods summary (DFT / wavefunction)

• DFT: fast, good for structures and many energetics. Functionals to try: ωB97X-D, PBE0-D3, B3LYP-D3, M06-2X. For noncovalent: ωB97X-V, revDSD double hybrids are excellent.
• MP2: sometimes good for noncovalent but overbinds dispersion; use spin-component scaled (SCS-MP2) or careful basis choice.
• CCSD(T): “gold standard” for single-reference systems (very costly). Use DLPNO-CCSD(T) for larger molecules.
• Double hybrids (DSD-PBEP86-D4, B2PLYP-D3) can approach CC accuracy at lower cost but are heavier than hybrids.

Special issues & diagnostics

• Multireference: if bond breaking, diradicals, transition metal complexes — run diagnostics (T1 > 0.02, large spin contamination, fractional occupations). Use CASSCF/CASPT2 or NEVPT2 if multireference required.
• BSSE: for binding energies, apply counterpoise correction or use large basis.
• Relativistic effects: include scalar relativistic corrections (DKH, ZORA) for heavier elements; spin-orbit for very heavy elements if properties depend on it.
• Solvent / environment: implicit solvation (PCM, COSMO) affects energies and geometries — use when relevant.

Example decision tree (short)

Practical tips (speed & reproducibility)

• Start cheap, then upgrade: geometry at lower cost, single-point at higher cost.
• Document everything: functional, basis, dispersion correction, ECPs, grid, convergence thresholds.
• Compare several functionals for sensitive problems (transition states, TM chemistry).
• Use composite methods (CBS-QB3, G4) for small molecules if you want accurate thermochemistry without CCSD(T) CPU cost.

Key references to cite / read

• Becke, A.D. (1993) — B3LYP foundational.
• Stephens et al. (1994) — DFT vibrational frequencies.
• Weigend & Ahlrichs (2005) — def2 basis sets.
• Dunning (1989) — cc-pVnZ basis sets.
• Grimme et al. — D3/D4 dispersion corrections.
• Santos Silva & Tenreyro (2006) — PPML justification (if using PPML idea analogously).
• DLPNO-CCSD(T) original papers (Neese et al.) for practical high-level single points.

(If you want, I can fetch precise DOIs/links for any of these.)

Final short recommendation (if you want one default)

For most organic / mixed small-to-medium problems, geometry: ωB97X-D / def2-SVP, single-point: ωB97X-D / def2-TZVP. For accurate reaction energies or noncovalent energies, add DLPNO-CCSD(T)/def2-TZVPP single-points and check BSSE.