TEC:

• 90% of the time you are going to want red button on your starbase...most players will assume you have red button and will avoid your SB like the plague, relying on a titans and bomber spam to wipe it out (if they even bother to destroy it)...
• It is common to see TEC SBs with both levels of red button, 1 or 2 hull upgrades, and nothing else...even trade SBs set up to extend your trade route through an uncolonizable gravity well can benefit from having red button if there's even a chance the enemy may be forced to phase jump close to the SB
• If you aren't going to use red button (or don't have the technology but need a powerful SB ASAP), it probably is to your benefit to go with all the hull upgrades, auxiliary government, and either weapon upgrades or strikecraft upgrades (depending on what you think your enemy will try to use to take out your SB)....
• SC are best to wipe out an opposing SB (usually an Orky) and caps bombing your planet (in which case build bombers) or to fend off enemy bombers (in which case build fighters)...weapon upgrades are better if you are getting rushed by lots and lots of frigates...

Advent:

• What you want on your SB depends on the type of fleet you think you'll be fighting...meteor storm + weapon upgrades is great against large frigate fleets while SC upgrades are better if you are dealing with bomber spam or mostly a titan/capital ship fleet (similar to the strategy explained above)
• Many people advocate mass disorientation....I'm very wary of this ability personally because it can be interrupted by things like the Kortul's disruptive strikes, the Radiance's detonate AM, and the Dunov's magnetize...
• Enduring Devotion is usually a good pick...as usual, maxing hull upgrades is a must...
• In certain situations you may want culture upgrades...if you've been driven back to your HW and cannot safely build a culture center (you don't have the slots or it would quickly get destroyed) then putting culture on your SB is a must (it's really embarassing to lose your HW to enemy culture)
• On the converse, a culture SB can be useful in overrunning an entrenched player's culture, especially if they are not Advent...

Vasari:

• If this is an offensive SB (such as a VR SB you will phase jump or an SB you are building at an enemy planet), hull upgrades and weapon upgrades are the best build...sometimes it may be to your benefit to sacrifce that 3rd weapon upgrade in favor of 2 upgrades for deflection shield or debris vortex, but usually that is not the case (neither ability is particularly good at defending against bomber spam)
• If you are trying build the SB at an enemy world while you are under fire, you may want to consider upgrading the weapons first, then hull....unless they are relying on bombers, the extra firepower helps remove the enemies firepower much faster and actually is better for preserving your SB than upgrading the hull first...you can use overseers and a skirantra with repair aura to help keep the SB alive
• Always keep in mind the option to put a stabilize phase space upgrade on your SB...this is immensly useful for SBs built at allies' gravity wells and it can be used to help reinforce an allies planet with your fleet at any time...

In general, avoid economic upgrades like colony pods and induced reverence...