PhD software recommendations
Based on my experience as a maths PhD student, I recommend Zotero and Overleaf software. Here’s a little information about each.
Zotero (resource management)
I managed all of the resources for my research (papers, books, etc) with Zotero. This software automatically extracts bibliographic information from library, journal and preprint websites and caches the corresponding pdf document with the click of a button.
I wrote my LaTeX documents using the online service Overleaf, which provides a vastly simpler experience than compiling LaTeX documents on your own computer. I also found the tool tikzcd-editor useful when creating commutative diagrams.