The following is a shortlist of general purpose elements that help you avoid gross modeling mistakes. All are accurate and fast if used correctly and with a suitable mesh.

1. B31 (for 1D abstractions)
2. CONN3D2 (for 1D abstractions of kinematic/dynamic mechanisms)
3. S4R (for 2D abstractions)
4. SC8R (for 2D abstractions with detailed analysis of transverse shear stresses, exotic)
5. C3D8R (when uncertain about using Abaqus/Standard or Abaqus/Explicit, >= 4 over thickness)
6. C3D20R (when certain about using Abaqus/Standard)
7. CSS8 (when using Abaqus/Standard for compression of thin structures, exotic)
8. C3D10 (when hex-meshing is not feasible)

For probably around a decade I have been using nothing else, except for C3D8RH, C3D20RH, and C3D10H when modeling fully incompressible materials.

Feel free to ask about the reasons for inclusion/exclusion of certain element types, but expect some "Read The Fine Manual" as answer, since this shortlist is an extremely condensed form of the information contained in our documentation.