The board there is overkill -- if you really want something with a Zynq including an Arm Cortex A9 that can run Linux, the Arty Z7 from Digilent is another Zynq board that's essentially a one-stop shop for this: https://store.digilentinc.com/arty-z7-zynq-7000-soc-developm...
However, for something as simple as an NTP server you could easily get away with an Arty A7: https://store.digilentinc.com/arty-a7-artix-7-fpga-developme...
From there you can instantiate either Xilinx's Microblaze MCU _or_ you could stick to Arm and use one of Arm's DesignStart cores (Cortex-M1 or Cortex-M3): https://developer.arm.com/ip-products/designstart/fpga/fpga-...
Glancing around Digilent's catalog, they've got an even cheaper Zynq board: https://store.digilentinc.com/cora-z7-zynq-7000-single-core-...