If I try and create a new merchandising rule in our store, there are no options in the "Fieldset" dropdown. I've tried adding a new fieldset, but still the same. Anyone able to give any pointers as to possible cause?

I believe merchandising zones use the field set you set in the configuration record

The custom record should be sourcing from a "Website Fieldsets" list judging by the form. The only reference I can see in configuration is Advanced tab, search results, "merchandisingZone" but adding a valid fieldset in there makes no difference.

Your Website Internal Name needs to match your website display name.

Thanks @PabloZ. The names were the same, but your tip allowed me to identify the issue. We have an apostrophe in our site name and this is obviously throwing an issue in the back end somewhere. Remove it and everything works as expected.