Configure CiviMember / CiviContribute for livery company quarterage fees
I'd suggest this setup:


Auto-renewed annual memberships (different membership types for each amount).
Fixed renewal dates (July 1).
Adjust the Membership Status rules to allow "Grace" status to extend several years (or whenever it is that you're ready to say good by to non-engaging members).


Memberships are often tricky because of language - if some of the default language needs to be altered, you can do that with the string replacement features.

1 + 3 will effectively mean your members don't really expire, since "Grace" status is considered 'current' (normally), but you'll have the renewal mechanisms for reporting and payments and notifications.