Equipment for a first batch
Updated
Short, cheap, and one item on it is worth more than the rest combined.
The short list
A mixing vessel with a lid, in a material your formulas will not attack. Stainless or HDPE.
An overhead stirrer with a suitable impeller.
Two scales: one with batch capacity reading to a gram, one to 0.01 g for minor ingredients.
A pH meter with calibration buffers.
Something to measure viscosity consistently, even if it is a timed flow through a funnel.
A filling setup: at minimum a jug and a funnel, better a gravity filler.
A torque gauge for capping, and an induction sealer if you ship.
Deionized water, or a way to get it.
What to spend on
The pH meter. It is the measurement everything else depends on, it is your batch release test, and a cheap one that drifts is worse than none because it gives you false confidence.
The small scale, because preservative and dye are dosed at fractions of a percent and under-dosing the preservative is a failure that reaches customers.
What to skip
A high-shear disperser until a formula needs one.
A heated vessel until you make something that needs heat.
A filling machine until several hundred bottles a run.
And a viscometer, at first, as long as you have a consistent alternative you actually use.
Dedicated equipment
Separate vessels and tubing for acidic and alkaline products if you can, because cross-contamination between them is an incompatibility rather than a flavor carry-over.
Separate again for anything fragranced.
And never use food equipment for this, in either direction. That is a rule with no exceptions.