Scientific papers are best written in LaTeX. This can now be done online, collaboratively, using Overleaf. Create an account using your unimelb email address to gain access to extra features.
The beamer document class can be used in LaTeX to create presentations.
Bibliographic software is required to keep track of papers you read and may wish to cite. I use Zotero but it is not the only choice. The two main features to look for are the ability to export bibliographic entries as bibtex so you may use them in your LaTeX articles, and the ability to click a button in your web browser to save the reference for you automatically.
If you use Zotero, you can set it up so the PDFs of the papers are stored locally and not synced to the web. (You have only limited online storage.) However, you can sync your papers to your different computers using your favourite file synchronisation software, such as OneDrive or GoogleDrive. I use SyncThing.
For most programming applications, scientific or otherwise, I recommend Python. There can be benefit in using it via a Jupyter Notebook. You can install this yourself, or use a free version courtesy of Google Research. Other choices for scientific computing are Matlab (if you must) or Julia.
A good editor is essential. I now use visual studio code regularly (except when I default to using vi which is undoubtedly the best editor ever).
Version control is important and for historical reasons we push to Bitbucket using git as the version control software of choice.
Calibre is highly recommended for organising your e-book collection.
If you are endeavouring to solve or explain a geometric problem, GeoGebra can help.