That is, the label of my choosing should be applied to all incoming emails notwithstanding the sender/recipient/subject/etc.
If possible, can the above be taken further wherein the label is applied only if it is destined for the inbox?
i.e. the email is NOT affected by a filter that "skip[s] the inbox".
Best Answer
The search
from:*will match any incoming message. A filter with that that applies a label should do what you want. (It seems to work just fine in my tests.)