I am writing my own DFT code using Gaussian basis and now I am writing the periodic boundary conditions (PBC). What integration grid people usually use for Gaussian basis PBC (+ reference please)? For isolated molecules, I used the SG3 integration grid with Becke's scheme to combine multi-atomic grids.
Exactly the same grids as for molecules, i.e. Becke grids. You just need to take the periodic boundary conditions into account when building the grid weights.
edit: e.g. PySCF has both molecules and periodic boundary conditions with Gaussian basis sets, and is in my experience a pretty fast code that is also easy to install.
The numerical grid implementations should be in https://sunqm.github.io/pyscf/_modules/pyscf/dft/numint.html for molecules and https://sunqm.github.io/pyscf/_modules/pyscf/pbc/dft/numint.html for periodic systems. Note: as usual for LCAO programs, PySCF implements PBC in 0, 1, 2, and 3 dimensions.