Reagent choice in the formation of Wittig reagent
I am fairly sure that for both, there are practicality issues at hand.
This is almost certainly so for the choice of phosphine. Even though PPh3 is absolutely terrible from an atom economy point of view, and even though PPh3O can be a real pain to remove after the reaction is done, at least it's a nice white solid which doesn't smell. On the other hand, the simpler alternative PMe3 is a volatile, pyrophoric, and extremely stinky liquid. PPh3 is also substantially cheaper than other alternative phosphines. (There are similar considerations for the Mitsunobu reaction which I have some experience with.)
As for the base, $\ce{BuLi}$ is just one of the most accessible strong bases to use. I don't think you can buy dimsyl sodium from the average chemical supplier. My suspicion is that the main reason why dimsyl anion is somewhat associated with the sulfur ylids is because E. J. Corey and his postdoc M. Chaykovsky popularised them together (e.g., Ref.1). Also note that $\ce{NaH/DMSO}$ mixtures are associated with significant explosion hazards (Ref.2).
Others with more experience will be able to give fuller answers.
References:

E. J. Corey, Michael Chaykovsky, “Methylsulfinyl Carbanion ($\ce{CH3-SO-CH2-}$). Formation and Applications to Organic Synthesis,” J. Am. Chem. Soc. 1965, 87(6), 1345–1353 (https://doi.org/10.1021/ja01084a033).
Qiang Yang, Min Sheng, James J. Henkelis, Siyu Tu, Eric Wiensch, Honglu Zhang, Yiqun Zhang, Craig Tucker, David E. Ejeh, “Explosion Hazards of Sodium Hydride in Dimethyl Sulfoxide, N,N-Dimethylformamide, and N,N-Dimethylacetamide,” Org. Process Res. Dev. 2019, 23(10), 2210–2217 (https://doi.org/10.1021/acs.oprd.9b00276).