My first legendary was the Shadow Price, with some pretty bad perks. And my first exotic was Hawkmoon from the week 2 Nightfall!
Now in destiny 2 I have all exotics and only use 4 legendaries in total, and I have no memory on how I got any of them.
EDIT: After seeing all these posts it makes me miss all the variety in weapons in D1 that made them memorable, from the name of the gun all the way to how the gun looked and performed. I do hope that down the line D2 will gain this ability for its future weapons.
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Got Ballerhorn week 2 I think. Shadowprice week 1. My favorite legendary besides the Crota scout.