Zinc – or galvanised steel rather than sheet zinc – would not affect the water. If it does, something is drastically wrong!
Water-tanks, garden equipment, cattle-troughs… of all kinds have been manufactured from steel and hot-dip galvanised for years with no deleterious effects.
If you want to fabricate the tank from plastic sheet, PVC is amenable to hot-forming and solvent-welding, so you can readily fit commercial PVC pipe and fittings to it using the solvent-adhesive sold for those. Be careful though: some plumbing parts use another plastic (polythene?) and their adhesive won’t work with PVC.
it’s best not to use whatever might look right in the kitchen departments of supermarkets: the plastic might not be what you think it is (unless the label specifies it). Design the tank to materials you can select and use appropriately. Some of our suppliers stock sheet plastics, so might have suitable ones.
While adapting a manufactured container only really works if you can find one of suitable size and shape.
If you want to use a cylindrical tank, consider a length of the toffee-brown PVC drain-pipe sold for underground duty – so made in a range of fairly large diameters. The ends could be the fittings manufactured for that purpose.
A further alternative is a fibre-glass one, laid up around a suitable former that could be of wood. It’s not something I’ve done so you’d need some research…. including how to avoid it sticking to the mould! Looking at fibre-glass mouldings they seem to have quite generous draught-angles to facilitate removal from the mould.
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As an example I built a fairly elaborate splash-back / motor-shield for my Myford lathe, from 3mm PVC sheet; heating with an electrical hot-air gun for bending, making “angle-plastic” for reinforcing the joints, and assembling it with plumbing solvent adhesive. A simple, shallow cylindrical embossing in one panel gives more air-space to the end of the motor, and was produced by using the bench-drill to press the heated sheet between two wooden formers.