I've carried out differential expression analysis with this data using the Limma-Voom pipeline. This involved calculation of TMM normalisation factors with edgeR::calcNormFactors, followed by voom transformation. I'm not sure if this approach is appropriate for eQTL analysis as it log2 transforms the counts.
For eQTL analysis, you can use any normalization method like TMM or log2(CPM) followed by quantile norm etc as long as its consistent across samples.
One key think is to remove known batch effects if you have any (e.g using comBat). Do some QC like PCA, plotting gene expression distribution per sample etc to spot outliers.
Another thing to keep in mind that you will be using PCs (or PEER factors) as covariates to remove any non-genetic effects on gene expression so normalization methods might have smaller impact. Sure, you may have some differences but top signals always remain with different norm methods.