I immediately set out getting all Genome skills I could immediately. I've currently collected all (except for Firaja, Blizzaja, and Aeroja), and I'm not yet through with Chapter 5.
Completion to me means doing everything I can. Completing the big things like side quests, levels, job levels, and the encyclopedia for items, enemies, and skills (Compounding everything) are naturally a part of it.
But I also can't leave behind any treasure chests, any items tucked away in a town, or miss any dialogue scenes. This last bit is made even more critical since the game has a system that tracks those. I know I can't get them all in a single play through, as some will change based on what order you do things, but I want to get as many as I can (currently, I think I've missed one, returning to the Vampire Castle with some of the Dragon Orbs, but not all of them).
Ideally, I'd also have at least eight of every weapon and shield (enough to equip every character with two of each), and four of each armor, helm, and accessory. But that is a minor thing, and I'll only really worry about it on equipment I really, really like.