How do you normalize RNAseq data for eQTL mapping?

I have 200 samples with bulk RNAseq data, from that I generated matrix of TPM values for each gene. I also have a matrix of expected alignment counts and a matrix of read counts.

I suppose I should use TPM for the eQTL mapping. If so, how do I normalize the values? Do I perform a quantile normalization or some other method? Should I even normalize the TPM matrix?

Additionally, what TPM cutoff should I apply and should I exclude genes according to X% of samples with TPM expression over Y_TPM_CUTOFF?

Thanks!