I think the first world would look much like it does now, except that fusion would replace most current nuclear, coal, and oil-fired plants - the technologies that supply base load. Natural gas plants will continue in service as fast response peaking plants.
Renewable energy sources will continue to replace older generation technologies so long as they continue to get cheaper and grid modernization keeps pace with the special requirements of renewables wrt variability.
All that depends on whatever fusion tech proves to be both technically feasible and cost competitive. If that doesn't happen, or is really delayed, then grid storage technology may win out as a cost-effective energy "source".
If storage becomes cheap and effective I'd expect to see renewables + storage expand to serve base load. Also, we'd see faster electrification of areas that currently can't afford classic distribution grids. This might accelerate significant changes in the developing world.
But whatever the generation technology, energy won't be "unlimited". There will always be cost limits.