For playing to win, what building/unit upgrades are the most helpful and which ones are a waste of time. For example, the Zerg Brood Queen seems worth the resources for the extra larva, but burrowing seems like a waste in a close game.
The Queen is not "research", it is a 100% vital in every game as Zerg. Unless you are rushing, you should be getting her immediately after your spawning pool finishes. Inject larvae as often as you can (you must be vigilant). Also the spawn creep tumor is very useful. Create 1 and use it to spread a "creep highway" across the map, which helps give you vision and get your units to their destination sooner.
The upgrades for each race depend on which build you go.
Absolute best upgrade is the slow for Marauders. Marauder's are a very powerful unit with the slow upgrade. They are an extremely strong unit especially with the slow upgrade.
If you get tanks, siege mode is definitely worth it.
Get your orbital command on your command center ASAP (not really a research, but an structure upgrade which is vital). Mules are amazing miners, and will get you about 300 minerals in their lifetime, so get them often and consistantly.
I hope these answers help you.
The answer is and always will be: It depends.
It depends on what your opponent is trying to do. It depends on what you're trying to do. There is no one "best" strategy that will work every time, and there is not an upgrade that is "never" useful.