Would there be a benefit to investing my learning in Fusion 360 vs. Aspire? Or learn both?
The more advanced you become, the more you'll find that there is no one software that will do everything well.
A lot of members here use Fusion 360, and a lot use Aspire. Both have their pros and cons.

Aspire is much better at V Carving, while Fusion has much more advanced toopath options. Aspire has tools for modeling 3D reliefs, which Fusion does not, but overall, Fusion 360 is a much more powerful modeler.

Does one or the other play better with Avid/Mach 4?
No, both are the same. The key is the post processor, which formats the g-code to match your machine. You can edit the post processor in either machine.
A lot of the default Fusion 360 post processors tend to send the machine to the Z axis home position, which causes issues for some people, but you can edit the post to remove this move.


My question here would be does Fusion define the home position or is the home position defined in Mach 4, and do they conflict with each other?
I believe you are talking about the origin, rather than "Home". Home is determined by the location of the machines home switches, and never changes.
The origin is defined both in the software, and at the machine. At the machine, you typically jog the spindle to the desired origin position, and zero the X and Y axis. This sets what's known as a work offset.

What does the workflow look like in going from design to cutting on the tool and is Fusion 360 or Aspire preferred and why?
Both the same. Create toolpaths from design/model, and export g-code. Load g-code into Mach4.



Since Fusion 360 is free, you might want to start there.
However, Vectric products can be faster to program, as their are far fewer options, and they are designed specifically to create gcode for woodworking projects.

As mentioned, you can start with V Carve Pro for a lot less money, and upgrade to Aspire at any time for the same cost as buying Aspire up front.