I would like to generate a clustered heatmap for my datasets to get a general idea of the expression profile of my cohorts, but I have both TMM and TPM normalizations. Is there a preference to which of these normalizations are better for this?
Anyway, I don't use any of them. When using edgeR, I use CPM - which can be calculated with function cpm() - to plot heatmaps. When using DESeq2, I use the "regularized log" transformation - which can be calculated with function rlog(). These transformations are applied to the counts already normalized by edgeR / DESeq2, so the values are robust to RNA composition (e. g. genes with very high expression being different between samples / treatments).
If I am trying to adjust for another factor, I would typically visualize multiple heatmaps (with or without centering by cell line or batch, for example).
Your question is a little different: I might compare the effect of TMM normalization on QC plots (such as sample clustering) and differential gene lists. However, after picking a strategy for a set of "initial" results, I would probably visualize the TMM normalized expression (if that was applied). That said, I would expect several rounds of analysis and discussion to critically assess your results, where your downstream steps (like functional enrichment) should inform the upstream steps (like normalization). So, I think you should probably have a more than one strategy that you've visualized before feeling comfortable with submitting a paper for publication.