  We consider a two-orbital tight-binding model defined on a layered
three-dimensional hexagonal lattice to investigate the properties of
topological nodal lines and their associated drumhead surface states. We
examine these surface states in centrosymmetric systems, where the bulk nodal
lines are of Dirac type (i.e., four-fold degenerate), as well as in
non-centrosymmetric systems with strong Rashba and/or Dresselhaus spin-orbit
coupling, where the bulk nodal lines are of Weyl type (i.e., two-fold
degenerate). We find that in non-centrosymmetric systems the nodal lines and
their corresponding drumhead surface states are fully spin polarized due to
spin-orbit coupling. We show that unique signatures of the topologically
nontrivial drumhead surface states can be measured by means of quasiparticle
scattering interference, which we compute for both Dirac and Weyl nodal line
semimetals. At the end, we analyze the possible crystal structures with a
symmetry that supports flat surface states which are effectively ringlike.
