Here's my advice. Keep items 1-5 in your list. Replace #6 with a Segger J-Link. Dump items 7-10.
The Eclipse/CDT/J-link tool chain is all you need to so serious, professional-level development work on ARM processors. It's all free except for the J-Link, and that's only $60 if you are not doing commercial work.
I do wonder why the Segger? Nothing against it, but the Nucleos come with a built-in ST Link debugger that works just fine. Well, maybe except for the programming via mass storage - that is a hit & miss gimmick for mBed crowd, but there is no need to use that. It can be even used to debug/program offboard targets in a pinch too.
The Nucleos work with either STLink or OpenOCD bridge software. I have posted the instructions (for a different Nucleo, but they all work pretty much the same) here:
https://www.eevblog.com/forum/microcontrollers/arm-starting-platform/msg988123/#msg988123The tutorials how to set all this up are all over the internet, it just takes a short googling. If you are using the GNU ARM plugin for Eclipse, it will even do most of that setup for you.
I would rather spend the $60 on something more useful, like a cheap logic analyzer, for example.