As I see it (this is just my interpretation as a reader), mastering spells seems to have levels. Much like Beginner, Novice, Advanced, Legendry, etc:
Beginner stage. Mostly the first, second and third years. They are in the learning phase. And they need to perfect their wand movement and pronounce the spells properly in order to execute them well.
Novice and advanced level:
The seniors. A very wide band. Most of the people in the magical world fall in these levels. Easy-to-execute spells and charms can be done with the swish of the wand.
Like, for example, Mrs. Weasely sets the washing process of the utensils with a small flick of her wand, etc. Prof. Lupin making the kettle brew coffee with a flick of his wand.
Mostly the mundane work can be done with a small flick or minimal effort. McGonagall waves the wand very lazily(to conjure up plates) when Harry and Ron had to have their feast in her office.
Doing advanced level magic with just a flick of a wand. People like Mc Gonagall, Dumbledore, Voldemort, etc.
For example, Dumbledore conjured up hundreds of sleeping bags with just a swish of his wand (in PoA), and so does McGonagall.
If there's a God Level, then it should be Dumbledore and Voldemort.
(However, insanely powerful spells(or curses) like Avada Kedavra takes a huge effort to pull off non-verbally, even for Voldemort).
For example, this quote from the Order of the Phoenix shows how powerful Dumbledore and Voldemort are, even with non-verbal spells:
"Dumbledore flicked his own wand: the force of the spell that emanated
from it was such that Harry though shielded by his golden guard, felt
his hair stand on end as it passed and, this time, Voldemort was forced
to conjure a shining silver shield out of thin air to deflect it"