A standard pipeline for DGE would be Salmon for (pseudo)mapping + DESeq2 for statistical analysis.
Salmon is one of a set of modern, fast and accurate mapping software. Requires a transcriptome to be defined.
DESeq2 is a mature R (Bioconductor) package which can handle reasonably complex designs, including time series, but not mixed models. The vignettes are ...
Note - This answer only covers the comparison of rA-dT (RNA:DNA) and rA-rU (RNA:RNA) duplexes, and not more exotic options involving deoxyuridine (dU) and ribothymidine (m5U).
I can think of three possible reasons why oligo-dT may be preferred over oligo-rU for poly(A) hybridization and mRNA capture:
The rA-dT duplex is more stable than the rA-rU duplex, ...
It depends on the definition of housekeeping genes.
ENCODE recently released RNA-seq of 17 tissues at 8 developmental stages.
A list of housekeeping genes was also provided.
They are not exactly constant. They just are less variable than other genes.