Look at the Edge actions applicable for your character's specialty. Do you want to do those right away or can you wait a couple go rounds to do it.
For social characters, there isn't much opportunity to gain more edge during an interaction. Maybe one or two. So if you anticipate a Social character using Edge (you should), you'll want to start with at least a Moderate Edge score to have a target re-roll hits.
Mages? Mages look to have several opportunities to gain edge. Reagents, Spirit Affinity, Analytical Mind for Heremitics, combat... Mage might be fine with minimal Edge to start and pick a few points up along the way. As there are no Magic Specific Edge Actions (yet), no real burning reason for high starting Edge.
Hackers. Analytical mind and not much else, especially against hosts. Probably want to start with a moderate amount to force re-rolls on Wild Dice from Overclock or on opposing success.
Combat characters. Anticipate is gold, if you're carting around guns start with 4 Edge or more. If you're a melee build Knock out blow and Shank are low cost so you're probably fine with just a couple.