These strategies might be outdated somewhat, fyi.
Your best strategy is to make use of your Distress beacons. If there are a bunch of enemies in a sector that has a bunch of unscouted sectors next to it, odds are good that more enemies are gonna fly in.
As such, use your Beacon to pull in their fleet from that 1 sector (assuming other surrounding ones are cleared!). The bad news is that they could come in anywhere on the map. Move into center of map to mitigate this issue, UNLESS you are long-range based.
Good news is that your weapons will be already primed and loaded so whey the do show up, and you can instakill one or two ships with a later game fleet.
You can also use beacons from a starbase which will help you fight and clear lots of bad guys.
Finally you can use a beacon to pull in an adjacent ALLIED SHIP into a fight.