I don't have anything conclusive to offer regarding system economies and BGS states, a lot of what I'm thinking may just be observer bias. For example, i suspect military systems might be more likely to offer missions for Weapon Test Data, because i found a lot in a system like that, but maybe it was just coincidence.
You're better asking
@Factabulous since he has done a lot of systematic data gathering on the topic.
One thing i strongly suspect though is when generating the mission board you're more likely to get more valuable/rarer materials if you are allied to them.
I think this is because how the reward generation system works. The mission is generated, then a value is assigned to it (with a dab of RNG), which takes into consideration your REP with the issuing faction. Now, imagine you're looking for Data X and its a rare data type. So in the system it has a value of 100,000. You are offered a mission for 50k, so it can't offer you Data X or any similar rare data. But if you are allied, maybe that mission is worth 100,000, so now it can be added to the possible rewards offered.
What this means if you will rarely see a data type you want if its rare and if you don't have good rep with the faction.
The downside to this is if you are allied but are looking for less rare data types, they are then competing in the loot tables with the higher rarity data types which are now spawning more.
I base this off my experience working in a system where i was neutral with everyone, doing lots of missions, and slowly as i increased in reputation with all the factions I stopped getting so many offers for certain data types and started getting more offers for things i was still needing and hadn't seen many missions for.
Maybe this is just RNG coming into play. Maybe its BGS states having an effect. Or maybe its really how it works.