What to buy before you start
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The equipment for skincare is inexpensive and the temptation is to spend the saving on more ingredients rather than on better instruments.
The short list
Two scales: one reading to 0.01 g for small components, one larger for the water phase. A preservative at half a percent in a small development batch is a fraction of a gram, and that is the most safety-critical number in the formula.
A pH meter, calibrated. A stick blender or small homogenizer, because emulsions need shear rather than stirring. Thermometers for both phases. Stainless or glass vessels. A sanitizer and a routine for using it.
The pH meter is not optional
pH decides whether the preservative is in its active form, whether the actives survive, and how the product feels. Strips do not give the resolution those decisions need.
Buy one with calibration solutions and calibrate on the day you use it. An uncalibrated meter is a confident wrong answer, which is worse than no answer.
What you do not need yet
A homogenizer beyond a good stick blender. A filling machine, until open time or check-weight drift says otherwise. A viscometer, until you are specifying viscosity to a packaging supplier. A laboratory of any kind: challenge and stability testing go to a contract laboratory and always will.
And not a large range of ingredients. Each one is inventory that ages.
Where to spend more
The small scale and the pH meter, because both directly determine whether the product is safe rather than merely pleasant. Then sanitation, which is not equipment so much as discipline and a suitable agent used for its full contact time.
Everything else can be upgraded when a bottleneck proves itself. Those two cannot be compensated for later.