> How do I get started using Emacs, if I wanted to use this awesome-sounding tool, while still being friendly to the fact that I have to get stuff done and still need the tools I mentioned above?

Only use the new system on Friday afternoons or whenever your typical slow periods or lulls happen until you get used to it.

If you plan to customize your workflow and extend your system I recommend:

https://github.com/SystemCrafters/crafted-emacs

If you want more out of the box, but harder to debug and extend I'd recommend:

https://github.com/doomemacs/doomemacs (you can use vanilla or vim keybindings)

In either case I'll echo the user recommending Mastering emacs.