They will fire
* the Tomahawk Land Attack Missile, which is being modified to hit ships at sea;
* the anti-air Evolved Sea Sparrow Missile (ESSM);
* the Standard Missile family — including the SM-3 for ballistic missile defense and the multi-purpose SM-6, capable of hitting aircraft, both cruise and ballistic missiles, or even ships;
* Future upgrades might add the new Long-Range Anti-Ship Missile as well.
The ship has enough space, weight, power and communications ability to enable easy addition of any advanced weapon system that is developed.
The Zumwalt has 14,798 tons of displacement and 78 megawatts of electrical power. The newest version of the Arleigh Burke destroyer has 9800 tons of displacement and 7.5 megawatts of electrical power.
In the longer run, the Navy is looking at an all-new destroyer or cruiser design built around the massive electrical requirements of future laser weapons, railguns, and other power-hungry systems such as radars.
The Navy has a plan to build Future Surface Combat ships. Those are still being designed but should start deployment in the 2030s. The Future Surface Combat ships will use a lot of Zumwalt technology.