As a gas utility guy I can say that 3-layer poly is not a common coating for most distribution applications. It is more likely to be used where the need for extremely high reliability (such as offshore) or resistance to abrasion (such pulling pipe through a bore) warrants the high cost. The extruded polyethylene (also sometimes called yellow jacket) coating is common and is much less expensive, although also less reliable. Fusion bonded epoxy (FBE) is common on some projects, particularly large, high pressure pipe where the extra expense is warranted. Pritec (wrapped poly over an extremely tough mastic (perhaps a butyl???))is also a great coating that is sometimes used. For almost any coating you select you should stringly consider supplementing it with cathodic protection by using sacrifical anodes, assuming the soil resistivity and other characteristics don't require use of impressed current. NACE has a lot of technical guidance available for your situations like yours.
Top coating the galvanized coating should include making sure that the top coat is compatible with the zinc. Not all coatings will adhere without special primers and surface prep, although it may be more of an issue for coatings typically used above ground. Although galvanized pipe below ground would not be my first pick, the galvanizing will provide some temporary resistance to corrosion where the coating gets damaged. You can always retrofit the pipe with C.P. anodes later.