We will mostly be making our own meals
How do you visualize doing this? I know nothing about Samoa but the combination "cooking facilitiesplace to buy foodbeing somewhere you want to be independent of first two" is not a good combination on Fiji. Budget end hotels with cooking facilities will be in towns like Suva or Labasa. Do you want to go to such places? There'll also be markets and stores in these places to buy things to eat.
You may find cooking facilities in more remote locations, eg at Lavena on Taveuni, and maybe some backpacker resorts, but there'll be next to nothing to buy since there are no stores in the usual sense of the word - and what you can find in the settlement is packets of noodle soup and tinned tuna. So you either have to bring in all your supplies or devote 2+ hours commuting on a bus to a village large enough to have a store. The shopping issue is still there even if you figure on using your own camping/cooking kit.
We're into culture ... interact with locals
I suppose we could discuss this for a while, what your expectations are, etc. Of course, I don't know what you're seeking in terms of 'culture'. Really, it's up to you, whether you take what you find or whether you're looking for a specific sort of experience. Fiji is a real place with real local people. They're not all wearing grass skirts and living out in the middle of nowhere in a stone-age setting. Some people are looking specifically for that sort of culture, the 'primitive' or 'traditional', fair enough I suppose but it can also be limiting. Even without that, Fiji is still an interesting place and Fijians have their own way of doing things. Church choir singing, for example .. I don't know where this fits on a scale of more or less traditional, but if you want to experience some culture ...
So, the more you can open up to how they live, the more you will discover.