Dissolving and blending
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The longest step and the one most often cut short.
Gentle and complete
The goal is everything in solution with as little air as possible.
Those two pull against each other: faster mixing dissolves quicker and entrains more air, and a foamed batch is one you cannot fill accurately or inspect.
So the answer is a slower vortex for longer rather than a fast one briefly.
Mixing that works
An overhead stirrer with a suitable impeller, below the surface, producing movement without a deep vortex.
Not a high-shear disperser unless the formula needs one, and thickeners are the case that does.
Warm water dissolves most things faster, and it also drives off fragrance and can damage some materials, so warm the water before the sensitive ingredients go in rather than heating the finished batch.
And add slowly. Dumping a viscous surfactant into water produces a lump with a gel skin that will sit undissolved for an hour.
What does not dissolve
Some powders form fish-eyes: a gelled outer layer around dry powder. Thickeners are the usual culprits, and the fix is dispersion technique rather than more mixing, wetting slowly into a vortex, or slurrying in a non-solvent first.
Some materials need heat, and some need a specific pH before they will go.
And some things genuinely will not dissolve in that formula, which is an incompatibility rather than a mixing problem and no amount of stirring fixes it.
Knowing when it is done
Clear, or uniformly the color it should be, with no streaking and nothing on the bottom.
Check the bottom of the vessel specifically, which is where undissolved material sits and where a paddle frequently does not reach.
Then let it stand until the air comes out, which for a foamed batch can be hours. Filling a foamed product gives you under-filled bottles that look full.