I'd say all of them are worth doing as it doesn't take a ton of effort to get them all done. You could probably put the extreme bar-tending and culinary credentials ones near the bottom of the list though.
Do run the consular authority missions -- once those are done you get the officer exchange missions. A good place to dump commons and bound uncommons (with the correct crits of course).
The biochemical investigations aren't worthwhile after the first two steps (those steps give great cxp) because the resulting consumables are practically free on the exchange, the cooking/bartending/gaming chains are only really worthwhile if you want the titles, and I don't remember what the cxp looks like on the colonial team (not star cluster exploration, the 3-step ones) to tell you if those are any good or not.
I'm thinking any of them that give you a repeatable mission at the end to get a blue or purple doff as a reward are worth it.
This. But if you're short on time, you can just do:
- Negotiate Delivery of Rare Commodities (even if you don't craft them, unpowered artifacts are worth 800k+)
- Facility 4028 (Strike Against repeatable gives contraband and prisoners that turn into guaranteed Blues/Purples)
- FED: Delta Voltanis & Zenas Expanse Support (crit on repeatable gives a DOFF that is good for getting more Support Crits)
- KDF: Khazan Cluser & Rolor Nebula Support (crit on repeatable gives DOFFs that are good for Maurading and Support)