How to choose the best method and basis set for a calculation in computational chemistry?
The experimental equivalent of your question would be: what kind and level of impurity am I going to accept in my experiment?

In terms of basis sets: in principle you keep increasing the complexity of your basis set until you reach convergence in terms of electronic energy. What you consider to be converged depends of course on your preferences.

With regard to the choice of method. Again, this depends on what you consider to be accurate enough. In heterogeneous catalysis, typically density functional theory calculations are performed using a PBE functional. This is accurate to about 5-15 kJ/mol which is fine in this field. This type of accuracy would be completely unacceptable in other fields. If high accuracy is required, people typically use post-Hartree-Fock methods such as MP2 or higher or CI.

My recommendation in picking a method and a basis set is the following:


Decide what you consider accurate enough.
Look into the literature if there are calculations being performed on the same or equivalent type of system and analyse their results.
Experiment using different methods on a model system. Look how the energy converges with respect to basis set and methodology. Pick the method that you think is best, both in terms of computational speed and accuracy. (it is OK to pick a couple of methods)
Perform the bulk of your calculations using this method.
If you are going to report your calculation. Clearly explain the reasoning why you picked a certain method. The potential readers of your report really appreciate to hear your motivation.