This is what you need to do, right from the start of the game:
-Before a mission, go to all systems available and "ping" them until reapers come out. (Obviously if a system is 100% resource depleted, don't go back).
-When you get the reapers coming after you, leave the system but try and ping on your way out because sometimes you can discover a bunch of crap as you fly out. Don't come back.
-When you scan the "first time", try and do it near planets as almost all the major discoveries are on planets and only fuel tankers are floating around elsewhere.
-Anything you discover but don't grab, will be there later (red circle). So if you have reapers on your ass but discovered something, just ignore it until after the next mission when the Reapers reset.
-Go do a single mission.
-repeate all of the above as all Reapers "reset" after a mission, allowing you to go back and search.

I finished with an armada strength around 4800 or so, almost full Paragon and all quests except the Eden Prime Colonists quests being done. There were 4 systems left that were not 100% but they were over 80%, so probably some fuel containers or something.

It was a bit of a pain in the ass because it sort of slows the game down IMO and doubly so when you have to fly back and refuel, but its fun also to build up your fleet.

 

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