As many previously said, there are two ways to answer this question.
If "primary" means most numerous, then the workhorse of the ZMSDF could be said to be the
Dragoon-class Strike Cruiser.
The Dragoon Class uses vertical-launch missile systems. Their CIC data allows them to launch both SSMs and SAMs, including the
Ultra Hedghog, a non-nuclear anti-submarine missile using MLRV-style technology.
However, if "primary" means most important, then we are talking about the three
Leonard Scamwell-Class Command Ships, based on the Sea Shadow class of the US Navy.
Such ships are armed, again, with VLMs. The high-stability SWATH design of the ships allows them incredible precision and rapid acceleration, making pinning down the ships non-visually difficult. Given their ability to attack from over the horizon and move before the missiles have hit their mark, they are highly important in anti-submarine warfare, provided their squadron's compliment of helicopters are deployed (or that the submarines are in one of the stationary SMBG sonar bands.)