I agree with Darvin3.
Structures and prototypes are essential.
Low level terran pop upgrades (skip other planet types unless you have a crazy map). One level of phase lane detection later on won't kill you (but always remember to be scouting). Wormhole only if it is strategically useful (depends on map). First level hull refinements. Phase jump inhibitors. Starbase constructors (e.g. Raloz for TEC).
But there are also some race-specific / ship specific upgrades that are necessary in my book as well.
These would not be relevant on a small map 1 v 1 or 1 v 1 v 1.
Some are more appropriate for an eco pocket player ion a big team match.
For Example:
For TEC:
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Hoshikos -> Demolition Bots
Kodiaks -> Intercept
Pervasive economy if you can swing it, it is huge ...
If Eco pocket player, logisistic buff (I forget name) and the labor negotiations (when transitioning to ships / warfare) and pervasive economy is then a must.
Advent:
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Repulse!!!!
Some improved reactor buffs for antimatter recharging can be useful for Advent ... (Advent fleets are devastating if the y have antimatter)
Some beam enhancements can be great for your bombers and if you crunch the numbers are more efficient than loading up on proportionally more drone hosts plus it buffs illuminators also! Remember SoaSE is heavily slanted towards. If I can I go pretty far down this line the illuminator buff is gravy, the meat and potatoes are the bombers. With this branch, I can skip using fighters (use telekinetic push + flak to thwart enemy strikecraft) almost entirely (beware Jam Weapons though).
Hangars + Shield Bestowal (forget the strikecraft; save the antimatter for the shields). Shield Bestowal works amazing with a starbase + repair bays. If done right Advent defensive positions are impregnable (i.e. all the opponent can do is go around).
Also the first couple culture updates and especially the evangelization node on starbases. These often force the other player to lay down multiple broadcast centers / media hubs per border world and chews up their logistic slots. Probably more efficacious the larger the map gets.
Lastly don't forget the Mass Disorientation for starbases, it is the ultimate fleet killer when supported by an advent fleet.
Also the tactics slot upgrade can be cost effective if you have to go more into defense until your fleet builds up.
Vasari:
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Phase missiles!!!
First couple of armor upgrades (in addition to normal hull upgrades)
Skirantras!!!
Hangars + Phasic trap (good night strikecraft)
Slave labor (especially on larger maps)!
Assault Deployment if you like parking an Orkulus in enemy territory
Some antimatter reactor enhancements are nice (think Skirantras)
Lastly did I mention phase missiles?
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Note I am ignoring the paths to end game super weapons like Novaliths, Kostura Cannons, etc. That is a personal choice and can be effective but can also be argued to be overkill. The exception being a Vasari pocket player who is fed to RA, which if played well is lights out.
Still in the end 3/4 of the full research trees are a waste unless you are in some huge drawn out game with nasty AI in a large map and even then you probably would have won anyways a lot earlier if you had built more ships instead of the extra research anyways.
I routinely am in last place in research when I play the AI (at almost any level). When in multiplayer I often see things the opposition has researched something vestigial and scratch my head saying "why did he waste resources on that"?