The most recent edition of LP to Fiji is better than the previous edition (which was very biased towards mid-range budgets and perceptions). The Moon guide to Fiji has long been the best and most comprehensive.
Backpackers in Fiji are of two types. The first are the low-budget holiday-makers and they're more likely to go to the Yasawa resorts and/or the Viti Levu resorts, and/or be onthe FeeGee Experience tours.
The other type are the ones most likely on a RtW trip, or ending a work holiday in Australia. They're somewhat more exploratory and adventurous. More chance of finding them on Ovalau or Taveuni, or anywhere else. Once you get off the main holiday track, Fiji can be very much your own.
The one thing to watch out for regarding domestic flights is the weather conditions. In a 2 month period I booked 2 internal flights, both within a week of departure date (Aug-Sept) and there were no problems getting a seat. But delays of some hours or even a day can happen because of rain or mist. So, try not to plan around tight connections.
As Laszlo said, camping really isn''t an option, not freelance. Some resorts, esp. low end, allow it on their property. Camp grounds are pretty rare. I saw only one, at Matei on Taveuni. Depending on where you are you had better be sure you have good rain shelter. If/when it rains it can be heavy and a simple tent won't stand a chance. If you want cheap accom, dorms might be more comfortable weather-wise.
For prices, check some resort/region links as a guide, such as
http://www.fiji4less.com/south.html
http://levukatourism-com.webs.com
While accom is easy to predict it is trickier with food. If you go to an island resort then you will be more or less stuck with the resort's meal plan. Holiday/tourist strips in tourist centers are rare to non-existent anywhere on Fiji. If you are in any town larger than a settlement, then there'll be some restaurants to choose from, usually of the fast-food, stir fry, food court types of things. And there'll be (super) markets and bakeries to put together your own breakfasts and lunches.