In the default configuration of most modern operating systems, IPv6 will automatically be enabled, if a router advertise to the LAN, that it can provide IPv6 access. This default is suitable for most scenarios, including yours.
If your current router does not support IPv6, then hosts on the LAN will not use IPv6 to talk to the internet. Once you upgrade your router, and the ISP starts supporting IPv6, then hosts on the LAN will automatically start using IPv6.
Not having an IPv6 connection towards the internet doesn't mean IPv6 is completely disabled. It just means it will only be used for communication between programs running on the same host as well as to some extent for communicating between hosts on the LAN.
Link-local addresses in IPv6 are often easier to work with than IPv4 because the IP address of a device is derived from the MAC address and remains constant regardless of configuration. And even if you don't remember the address, you can just ping ff02::1 to find all addresses on the LAN.