Computer Operations for mining, management and Leadership for production and Government factions and piloting are pretty much the only required skills now. Diplomacy/leadership at 5 is possessed by half the galaxy.
At some point we will get R&D and combat at which point they will soon come in handy to have skills in as well. Bare in mind if a skill is useful now many people wil have it but if it is needed in a while it will be more useful to everybody then.
Just do what many others do and just dont spend skill points on the now and invest them for the future.
Repair is very underestimated in my opinion, so far it only work for recycling barely (it makes trivial difference) but eventually it should help repair entities faster and better, which will be in demands when things begin to get damaged.
Moons can't fly.
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Computer operations is good for prospecting, not really mining - you want leadership for that to reduce costs. Personally I feel that the diplomacy skill is not particularly useful - it reduces costs of hiring NPCs and slightly reduces construction times, but I think it's only useful putting a point or two into it, if that.
R&D should be useful come R&D but who knows when that will be. Combat skills will be quite important considering ground combat is relatively close for PvP, depending on if you want to get into that.