Only 70 points are required, and the three highest rewarding support quests add up to exactly 70 points (Please Find My Cat [30 points], Please Find My Cat 2 [10 points], Kappture the Kappa [30 points]). They're all available from the start of Part-Time Hero, though Please Find My Cat has to be activated by returning to the Part-Time Hero office and two of the kappa statues are locked until reaching chapters 6 and 7.
Alternately, the Missing and Shit Out Of Luck tasks award 43 and 15 points in total, with Missing just requiring tracking down 5 people and Shit Out Of Luck requiring delivering 21 packets of tissues, which costs 4200 eco-points.
Altogether these tasks should award about 120 points in total, giving a lot of wiggle room