Which systems give the most blue options for events?

Solution 1:

There's a nice list of all the blue options, sorted by upgrade / crewmember, on the FTL Wiki, but I'll summarise the results here.

Based on the count of possible blue options per upgrade, the following are the choices most likely to give you blue options:

• Augmentations - Long Ranged Scanners, by far

• Crew - Lanius, with Slug second

• Drones - Repair

• Ship - only one blue event, with the Rock Ship

• Sub-systems - Sensors

• Systems - Medbay (Hacking and Teleporter rank highly too)

• Weapons - Fire Bomb or Missile

This does not take into account the relative frequency of the events for which a blue option appears, nor the required level of system upgrade required for the blue option to work / be available, nor the relative ease in obtaining / starting with any of these options - but choosing from these upgrades (and generally aiming for at least level 2) will give you the best chances, if that's what you're going for.

Bear in mind that not all blue options are necessarily best or even effective options, either; for example, I recall an event where a ship asks you to donate missiles, and with a missile weapon equipped you can offer to fire one at them. Understandably, they're not keen on that idea.