  The success of HI intensity mapping is largely dependent on how well 21cm
foreground contamination can be controlled. In order to progress our
understanding further, we present a range of simulated foreground data from
four different $\sim3000$\,deg$^2$ sky regions, with and without effects from
polarization leakage. Combining these with underlying cosmological HI
simulations creates a range of single-dish intensity mapping test cases that
require different foreground treatments. This allows us to conduct the most
generalized study to date into 21cm foregrounds and their cleaning techniques
for the post-reionization era. We first provide a pedagogical review of the
most commonly used blind foreground removal techniques (PCA/SVD, FASTICA,
GMCA). We also trial a non-blind parametric fitting technique and discuss
potential hybridization of methods. We highlight the similarities and
differences in these techniques finding that the blind methods produce near
equivalent results, and we explain the fundamental reasons for this. The
simulations allow an exact decomposition of the resulting cleaned data and we
analyse the contribution from foreground residuals. Our results demonstrate
that polarized foreground residuals should be generally subdominant to HI on
small scales ($k\gtrsim0.1\,h\,\text{Mpc}^{-1}$). However, on larger scales,
results are more region dependent. In some cases, aggressive cleans severely
damp HI power but still leave dominant foreground residuals. We also
demonstrate the gain from cross-correlations with optical galaxy surveys, where
extreme levels of residual foregrounds can be circumvented. However, these
residuals still contribute to errors and we discuss the optimal balance between
over- and under-cleaning.
