Your question is poorly explained: what downstream analyses you intend to perform? Are you moving from within-sample comparisons to differential expression analysis?
I believe DESeq2 does not perform quantile nor median normalization, only limma.
About limma between-array normalization: quantile normalization is performed to make the distribution of microarray intensity signals the same between all arrays being analysed. Median normalization (
method="scale") makes the samples to have the same median.
DESeq2 and edgeR normalize for library size, each package has a different method for performing the normalization, but the idea is to make all samples sequencing depth "the same". DESeq2 uses some transformations (
vst) for exploratory analyses and visualization, but these are not used for differential expression analysis.