Before buy and setup/install recommend also reading tips as really apply to all to all Zigbee solutions:
https://github.com/home-assistant/home-assistant.io/pull/18864
You can use ZHA (natively integrated into Home Assistant), deCONZ (requires an external deCONZ or Phoscon exist), or Zigbee2MQTT (requires existing Zigbee2MQTT and MQTT). Read integration docs:
https://www.home-assistant.io/integrations/zha
https://www.home-assistant.io/integrations/deconz/
https://www.home-assistant.io/docs/mqtt/discovery#support-by-third-party-tools
https://www.zigbee2mqtt.io/guide/usage/integrations/home_assistant.html
Yes all different Zigbee solutions (ZHA, Z2M, deCONZ) require you to buy a Zigbee adapter and some Zigbee solutions support many different types of Zigbee adapters while others only a few or just one.
Correct termenoloty for this type of Zigbee gateway/bridge/hub adapter is a “Zigbee Coordinator”, see:
https://www.home-assistant.io/integrations/zha#compatible-hardware
https://www.zigbee2mqtt.io/information/supported_adapters.html
Note that you can use different Zigbee solutions at the same time but they will each need their own dedicated Zigbee adapter and every solution will only set up a single Zigbee network and it is not possible to connect different Zigbee networks so they will not be aware of the others in any way.