Best system be default is Duzahk. Unless it is somehow heavuly randomized and consists of huge, high grav planets only.
Duzhak only has 2 planets in it by default, and neither are particularly well suited to first colonies.
Everything else is entirely procgen, and as some folk have shown can have some stunning opportunities.
It's p. much always worth stopping by Duzahk early just to see if there's anything interesting there.
...I may be missing the potential of some of these systems.
Might be helpful to say what's on those gas giants. They're often a useful source of volatiles.
Breakdown of systems:
Damar system:
Spoiler
Eros: Terran 50% farm +2 rare ore -1 organics +1
Kepheus: Desert 125% Deciv vast ruins farm -1 ore +1 organics 0
Minnow: Barren 175% ore -1
Gas Giant: yes
Eros will grow quickly and produce a decent income with just farming and mining.
Kepheus will lag behind a bit and will have a smaller (though still useful) income via mining.
Minnow is entirely ignorable unless you want some extra industry slots.
Gas giant may or may not contain enough volatiles to support fuel production, but there isn't enough ore in this system to support a refinery in any case so you're still dependant on imports.
If you're just looking for a money farm and somewhere to store stuff, this system will serve you well.
Gualechis System:
Spoiler
Mesh: Jungle 75% vast ruins farm +1 ore 0 organics 0
Zuan: Volcanic 225% rare ore -1 ore +1
Telephasa: Volcanic 200% rare ore +3 ore 0
Asmaidas: Toxic 225% rare ore +3 ore 0
Gas Giant: no
Mesh will make a decent homebase with a good income via farm + mine.
Colonising Zuan plus Telephasa give you access to enough ores to run a refinery without imports. Although neither will grow quickly so your production will be limited by your mining colony size.
Ignore Asmaidas as it's a worse version of Telephasa.
No gas giant, plus no volatiles means no native fuel production. You can still always import volatiles.
A decent money farm system, but the ores being on separate mining planets are less than ideal.
Lempo System:
Spoiler
Gray Ghost: Arid 100% farm -1 ore -1 organics 0
Fenrir: Tundra 100% Farm -1 organics 0
Magon: Toxic 225% ore 0 vollatiles 0
Iravik: Rocky Metalic 200% scattered ruins rare ore +1 ore 0
Fared Kathon: Rocky Metalic 200% rare ore +1 ore 0
Gas Giant: no
Gray Ghost and Fenrir are p. much interchangable, and either would make a decent home base. With -1 food you'll need to make sure you make one your first colony and max boost growth so it's always your largest so you never have worry about food imports.
Magon is nearly useful, just not quite enough volatiles. It would still make an okay amount of money from mining exports.
None of the other planets are all that interesting.
There isn't enough ore to run a refinery so you'll need to import, and there's not enough volatiles so again, import.
Take the 2 good planets and put farm + mine + military on them, plus whatever else you feel like when they grow.
Clix System:
Spoiler
Merlin: Eccentric Terran 125% Pollution scattered ruins farm +1 ore 0 organics 0
Dargor: Rocky unstable 200% rare ore +2 ore +3
Jiao: Toxic 200% rare ore -1 ore 0
Galavar: Barren 200% ore +3
Gas giant: yes
Merlin would make an okay first colony, and pull in a decent income with farm + mine. Growth will be a bit slower due to the hazard.
Dargor is an excellent mining world with enough ores to run a refinery with no skills or boosts. Mine + refinery would be a good combo here.
Jiao and Galavar are mostly ignorable.
Gas giant may oy may not contain a useful amount of volatiles.
Fairly decent system. If the gas giant has +1 volatiles or more it could be entirely self-sufficient.
Beta Chirra System:
Spoiler
Beta Chirra 2: Terrran 125% farm +1 rare ore +2 ore 0 organics +1
Beta Chirra 2: Volcanic 250%rare ore +1 ore +2
Gas giant: no
An okay Terran world. Not great hazard, but a decent spread of resources. Would make a good amount of money with just farm + mine.
The Volcanic world would make a decent mining colony. And both together would be able to run everything except fuel production due to the lack of volatiles.
With just 2 planets in the system you'll need military bases on both, so you'll need to pump that volacanic with as much growth boosting as you can so you get enough industry slots.
Gamma Persai System:
Spoiler
Gamma Persai II: Eccentric Terran 125% Farm +2 rare ore -1 ore -1 organics +1
Gamma Persai I Vocanic 200% rare ore +2 ore +3
Gamma Persai B I: Barren 200% Scattered ruins ore +2
Gas Giant: no
Again, this system can do everything except fuel. The Terran E. would make a decent income on it's own.
The barren is useful due to ruins, and providing more space for industries.
Better than Beta Chirra imo.
Delta Dumir System:
Spoiler
Delta Dumir II: Desert 125% ore 0
Delta Dumir II B Desert 150% ore 0
Delta Dumir II A Desert 125% farm -1 rar ore -1 ore -1 organics 0
Delta Dumir I: Rocky Metalic 175% ore +3
Gas giant: no
Three low-ish hazard planets make an interesting system with lots of flexibility. IIA would need to be your first colony to make sure its the largest so the poor farm can feed everyone though.
There's enough ore to run a refinery if you colonise the rocky world, but still not enough rares. So that will have to be imported. Might be better ignoring it and just importing both tbh.
No volatiles so you'll have to import those if you want to make fuel.
This system could become a military powerhouse, if you don't care about being dependant on imports.
Kigatilik System:
Spoiler
Suroclaire: Terran 125% scattered ruins farm +1 rare ore -1 ore 0 organics 0
Xaphasor: Irradiated 200% rare ore +3 ore +3
Sar: Volcanic 275% rare ore +1 ore +2
Loka: Volcanic 250% rare ore +2 ore +1
Indrik: Volcanic 200% rare ore +1 ore 0
Gas giant: yes
Suroclaire is a fair pick for a home base. Would have decent income, but slightly slowed growth.
Xaphasor is an excellent place for mining & refining.
Both would make a ton of money.
The other planets are more-or-less ignorable unless you desperately need more room for industires.
The gas giant, if it has more than +1 volatiles would give this system complete self-sufficiency.
I'd go for either Cilix or Kigatilik due to the possibility of having all resources. But honestly any of those could work for just pulling in a decent income.