From ancient memory:
Each race is 3 sectors deep. Homeworld, core and border. To distinguish the 3, I used the shipyard. 3 ships per class in yard = homeworld, 2 ships per class = core, 1 ship per class = border.
You realistically can only "flip" sectors while at war.
Every time I seriously threatened to flip the enemy's homeworld sector, they'd sue for peace and I'd be stuck running home, as suddenly my ability to threaten a flip was removed.
Also, each race has a specific "unexplored" sector. From what I remember, for Feds it was the northernmost "border" sector, right there at the top of the map. For Rommies, it was the furthest SE corner. These sectors have no base (no resupplying / new ships), but running missions there increases your economy value a lot more than running missions in enemy space...