I've only had a few hours to play since the release (only capital I have is an executor), so I haven't really gotten to test many ships, but I have spent some time theory crafting since I got a giga cannon pretty early on.
I feel like there are very few ships that want to use the giga cannon. It's a low DPS efficient large energy, so IMO more of a 'support' weapon (providing very good armor cracking). There's very few ships that really want to spend a large energy slot on a more supportive role. I think the only real candidates are paragon and radiant, because they can quite easily spend their entire flux budget without using all their large slots. I think giga cannon will also pair well with a cryo blaster and auto pulse lasers.
I'm also a bit curious about using it on an odyssey. I think for the player, double plasma will still be king, but for the AI, it might be interesting. Maybe something like plasma + gigacannon + a few IR pulse lasers + kinetic missiles. I would be surprised if it was better than alternative though.
On radiant, my first thought would be 4 auto pulse and one gigacannon (or maybe 3 and 2), and then some mix of IR autolasers, gravitons and maybe a cryo blaster in the mediums. Could also get armor damage from missiles in the medium synergy slots, but I feel like not having to invest OP in missile hullmods would be helpful. If you are s-modding expanded mags, you could throw in mini-pulsers or ion-pulsers as well.
For paragon, I would want 2x autopulse, 2x giga cannon, 2x heavy needler, ion pulser and cryo blaster. I think that would be pretty decent. Paragon seems like the best candidate since it can use fortress shield while weapons are recharging.
I guess zigg is also a candidate, but I feel like DPS is better (plus I hardly use zigg because it doesn't feel fair/fun after the initial rush of murdering everything a few times).