Equipment for a first batch
Updated
Short until you add cold and carbonation, at which point it is the most equipment-heavy property here.
The short list
A vessel you can heat, with a lid.
A fermentation vessel, if you ferment, with an appropriate cover.
A thermometer, a pH meter with buffers, and a refractometer or hydrometer for Brix.
Scales.
A way to chill: at minimum an ice bath, realistically a fridge or a chiller.
A filling arrangement, a capper, and bottles.
Sanitizer, and somewhere to sanitize bottles.
What to spend on
The pH meter. It is the safety measurement, the batch release test and the earliest warning of a problem. A cheap one that drifts is worse than none.
Chilling. It is required for carbonating, for arresting a hot process and for holding finished stock, and it is the constraint that most limits a small operation.
What to skip
A counter-pressure filler, until carbonation is actually the product.
A heat exchanger, until volume justifies it; a pot and an ice bath work at small scale.
A canning line, which is what mobile canning services exist for.
And a large fermenter, since capacity here is vessels times turnaround rather than one big tank.
Shared kitchens
Worth considering seriously in this category more than most, because the expensive items, cold storage, a licensed premises, sometimes a pasteurizer, are exactly what a shared facility provides.
The constraints are scheduling, shared equipment and cleaning standards you do not control, and for an unpasteurized product those matter.
Ask specifically about cold storage allocation, because it is the thing you will run out of first.