I hope you are speccing NSF-approved coatings only.

i tried to feel out the crowd myself a few months ago on this for immersion coatings...
thread332-344253: zinc primers for interior water tanks

My gut feeling is that zinc primer and epoxy primer systems both work fine, all other things being equal. Regardless, there are enough tanks out there for both to say that zinc-epoxy-epoxy and epoxy-epoxy-epoxy are both the "Standard" system you asked about. unless you go down the path of extending coating life with plural-components, the tank will be getting recoated in the next 10-15 yrs anyway.

If you want the same system for multiple manufacturers for bid purposes, pick a 3-coat epoxy system since everyone has it. If there is preference for zinc primers by the owner (i'm going to go on a limb and assume you aren't die-hard entrenched in one or the other), exclude the non-player manufacturers. If there is no preference either way, list all the approved manufacturers and let the contractor choose the system. the owner will likely have a preference to few certain name brands already.

if these are new tanks, look into having the plate metal shop primed except weld heat zones... you'll cut down on surface prep in the field and probably get a better prime.

my $0.02. i hear a lot of opinions about those primers but i just don't see many case studies or hear stories about how well or poorly "that zinc coated tank" is doing.

I've specified painting systems for navigation lock gates and dam gates for many years. We always used 2 coats of epoxy for immersion service, and zinc-rich with epoxy and a polyurethane topcoat for splash-zone stuff.

I am using a zinc primer for my water tank, and it works very well. But what works for me, might not necessarily work for you. Anyways, good luck.

Keep in mind that specifying a "zinc primer" is about as specific as specifying a "concrete bridge"