My favourite resource hands down is Economy resources. They tide me over my $$ woes, until I get the more advanced governments. Also they are always handy and useful throughout the whole game.

Next is morale, but late game, I can easily keep my morale at close to 100% easily without this resource and with high tax rates.

Research resources don't seem to do much for me not sure why, don't seem to speed up my research too much, though the full 30%?? should be significant??

Influence resources are great , they are enough to make colonies within my influence move to 'pirate symbol' but takes a while for them to flip.

Military resources I find are less useful early game, where you are armed with low value weapons (1-3 attack), so the bonus (rounded down), comes to almost nothing. Once you start hitting ships with 6+ attacks , military resources start to kick in by adding 1 point here and there.