During the course of the campaign, you'll unlock a number of research options. As soon as you get the lab, about five missions in, you can see all of the availible options, but they are split up into pairs so you can only obtain half of them. Here are my suggestions.
Zerg Tree:
First Tier: Bunkers
Either bunker upgrade is fairly awesome, but since Bunkers need such continual repairs either way, I would go with the added firepower, and trust your SCVs to keep them up even without the health boost.
Second Tier: Defenses (Planetary Fortress versus Perdition Turrets)
Perdition Turrets, hands down. A cheap, effective, easy to use firebat turret instead of a bulky, powerful, but nearly useless cannon. The Fortress can't fly, and is expensive as hell. Your Command Centers are nearly always in the safest part of your base anyway, so the most the fort can do is protect your SCVs, which it isn't that great at since splash damage will kill them. Building a Fortress where you might use it is laughable, since other defenses are way better and much, much cheaper.
Third Tier: Extra Units (Predator versus Dropship [don't remember Dropship's full name])
Honestly, I'm not too thrilled with either of these units. The Predator is fairly nice against the Zerg, but it's hardly a can't do without unit. The Dropship would be awesome, except that by the time I've teched up to the Starport, I'm not using ground units for my assaults anyway (or if I am, I'm slogging them around on the ground, not airlifting them). I'd stick with the Predator. It comes around a little faster, and has a little more overall utility.
Fourth Tier: Upgrades (Extra Energy versus Vehicle Self-Repair)
Go with the extra energy. Self repairing vehicles is nice, but very slow, and a certain Protoss Tree research option blows this ability completely away. Every energy unit gets more energy, and start with more energy, so your casters have a lot more firepower to work with.
Fifth Tier: Anti Zerg Defenses (Mind Controller versus Slow Totem)
Both of these are just cool. The Mind Controller lets you tag a friendly Zerg unit and control it permanently, and if you get a good unit, it helps a ton. Best of all, these caught units don't add to your Supply total, so you can slowly build up an army of nearly limitless Zerg, if you can keep them alive after your capture them, they'll self repair or your medics can heal them (even Ultralisks). It doesn't work automatically, though, so you'll have to manually trigger it.
But the Sigma Radiation Tower is also cool. Slows Zerg movement by 50%, so they take twice as long to get to you. That's twice as long to get through your Siege Tanks and other defenses lines of fire. Then, they suffer 50% attack speed reduction as well, which means they won't tear through your defenses nearly as quickly. This is great, especially on hold the line missions.
Advantage goes to the Sigma Tower, but both are really useful.
Protoss Tree:
First Tier: Upgrades (Weapon Speed Boost versus Health Boost)
Basically, this one improves the quality of the weapon/armor upgrades researched at the Engineering Bay and the Armory (adding in a secondary bonus of attack speed or health of 5% per upgrade), and is fairly evenly split. Personally, I prefer the higher attack speed that the weapon upgrade gives, but it's a fairly close call. Boosts are % based, so they affect units fairly well, regardless of tech tree position.
Second Tier: Economy (Faster Vespene Harvests versus Instant Build Supply Depots)
Well, sure, supply depots take a little while to build, but its rare that I need them built immediately. While increasing the rate of Vespene harvesting lets you tech up and build higher quality units that much faster, and, for me, it's the way to go.
Third Tier: Economy Mark II (SCV Reactor versus Automated Refineries)
This one is a fairly unbalanced one. Automated Refineries free up 3 SCVs per Geyser to spend on Minerals. Producing two SCVs is nice, especially for startup, but given how many missions you need a steady stream of Vespene incoming, making it come in without tying up SCVs is a huge boon.
Fourth Tier: Flying Detectors (Nighthawk versus Science Vessel)
In the entire research department, there is no simpler choice than this one. The Nighthawk is a sweet unit, don't get me wrong. But the Science Vessel is just allmighty in SCII. Why? It's a flying SCV that repairs vehicles and infantry at the cost of energy, not minerals/gas. And it can repair a lot. Grab two of these (so they can repair each other), and you can have them keep your entire air wing alive forever. These things are fast enough to keep up with your other air units (and significantly faster than Battlecruisers, something to watch out for if you group them together, you don't want Science Vessels to reach air defenses before the Battlecruisers), have enough energy to heal basically forever, and generally just make your missions way, way easier. They can Irradiate biological targets if they have to, but, really, with them healer the damage dealers, there is no need for that.
The Nighthawk, on the other hand, is a powerful caster, but severely more limited. Three neato abilities, but it can run out of energy much faster, and is a bit of niche unit. Hunter Seeker can't target buildings, and its splash damage makes it a little useless on defense. Auto Turrets are ok, but don't do tons of damage and don't last long. The most useful, and most difficult to use, is the Point Defense Turret, a little aerial drone that shoots down 30 projectile attacks before running out. Great, in the right situation, and before it runs out of energy.
So, definitely, definitely, go with the Science Vessel. They are reasonably cheap (although they require an upgraded Starport), and they make your assault forces basically immortal. As I said, this thing negates the need for regenerative armor from the Zerg line, and the extra energy benefits the Science Vessel to keep it casting.
Tier 5: Convenience (Infantry Drop Pods versus Reactor/Tech Lab combo)
The Drop Pods are nifty, and if you use primarily units from the Barracks, you will probably want them. Drop pods make all Barracks units build instantly, and they drop on the rally point, so if you set the rally point on your assault forces, you can keep them reinforced as long as you have the credits. Definitely a powerful tool.
My favorite for this one, though, is the Tech Reactor. This thing lets you build two queues worth of high tech units. Rather than being stuck with just Marines, Vultures, Hellions, Medivacs, and Vikings in your double queued structures, you can now double queue any unit. From Firebats to Battlecruisers, this upgrade doubles the production capabilities of all the high tech units, and only costs 50% more than the standard Tech Lab or Reactor. Definitely a plus, as you'll see when you start cranking out huge teams of Siege Tanks and Battlecruisers (with accompanying Science Vessels, of course).
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