Campaign

Warning, possible spoilers ahead!

I won't say much on the WoL campaign, as there are already tons of good guides for it, but I do have a few tips.

1. It never changes. None of the updates after release apply to it. the units will always behave in the same way. (Not everyone knows this)
2. After you get picked up by the Hyperion, play the missions Smash and Grab and The Devil's playground first. This gets you the Reaper, which is ideal for the first two Colonist missions.
3. When Zeratul pays you a visit, do all his missions right away. Because they're not part of the standard campaign, what you do in the rest of the campaign won't affect them. However, the research boost they give you will allow you to access the higher tech abilities much earlier and will have a major impact on the remaining missions.
4. The enemy attacks on a timer. If you can understand the timing, you will be able to predict their attacks.

With The HotS campaign, however, I have a lot to talk about.

Kerrigan

To start with, let's take Kerrigan's abilities.  On tier 1, I found Kinetic Blast to be extremely useful throughout the entire campaign from start to finish, taking out dangerous units like siege tanks and immortals instantly, and minimizing your losses. While the other abilities on the tier are great, they aren't as useful. For example. Heroic Fortitude doesn't work if Kerrigan isn't getting hit frequently, and in my case she got hit only rarely. 

Evolution Pit

A large portion of the evolution choices available to you in the campaign are based on a simple concept: are you going to send your units out in mixed groups, containing some of everything with each unit specialized against a different enemy type, or are you going to send out squads that contain only one soldier type? This simple distinction makes it much easier to make your permanent decisions.

For Banelings and Zerglings, always get the leap-charge strain. The reason for this is simple. as far as I can tell, from watching both troops in action, when the unit is in the process of leaping towards its target, it becomes untargetable. the leap ability messes with the units on the other side, making the units in mid jump (and in the vital stage of closing the distance on a ranged enemy) almost invincible. This bug (it has to be a bug) means that a unusually high number of units will make it to melee range, increasing their effectiveness and lifespan. In addition, these strains do a much better job of not getting in the way of the rest of the army and each other, reducing the clog caused by choke points.

For the Zergling strains, in a raw dps comparison, vs. 0 armor, 2 raptorlings have the combined attack of 14, and 3 swarmlings have a combined attack of 15. vs. 1 armor, they both do 12. in other words, swarmlings do better against unarmored units, but raptorlings are better against armor of any kind, which in the later missions is quite common. As for the three mutations, take your pick. They all work well.

For the Baneling strains, get the mutation corrosive acid. doing double the single target damage makes them much more effect at 2 things: taking big units down, and Turtle Busting. The bonus applies to the anti-building enhancement as well as the base attack, and allows only 3 Banelings to destroy a bunker. 

Rupture (+50% splash radius) doesn't help a Baneling's dps that much, and they have a tendency to run ahead of the rest of the troops, making Regenerative Acid ineffective unless paired with Zerglings, in which case it works quite well.

For the Roach strains, it all comes down to whether or not your roaches will be going out alone. If they are, then the Corpser strain ( which generates an infinite meat wall of roachlings) plus tunneling claws (moving + double regen while burrowed) are the way to go. however, if you intend to send them out with Hyrdalisks and Ultralisks or Zerglings, then you want the vile strain (it makes enemy units move and attack 4 times slower) with  hydraulic bile (+8 damage vs. light units). Adaptive Plating (+3 armor when under half health) does not increasing their survivability enough to be worth selecting

For the Hydralisks, the mutations are all about the same choice as the roaches. If they go out alone, you want ancillary carapace (+20 life). frenzy and grooved spines are used in a group. 

The evolution tree, however, is different. You get to choose between an anti-armor, single target lurker (a creature the burrows and then sends out attacks underground), and an anti-light, Area of Effect (AoE) lurker. Both Lurker strains are excellent at defense. The decision between them will be based on the contents of the rest of the swarm. if you are lacking in anti-armor defense, or want to use the lurker as a siege unit, you want the Impaler strain. If you are lacking in anti-light defense, or love the devastating AoE (it will kill an enemy force much faster than the Impaler), the Lurker strain is what you want.

For the Swarm host, the mutations fulfill three distinct goals.

1. Burrow makes the swarm host invisible to all non-detectors, increasing survivability.
2. rapid incubation removes the 3 second delay between the death of one wave of locusts, and the spawning of the next, increasing dps and lifespan.
3. Pressurized Glands allows locusts to hit air, meaning that the swarm host can now defend against everything.

This unit does not have an easy evolution choice. The Carrion strain is the more combat worthy of the two, producing flying locusts that have 25% less health, 50% more damage, can see over cliffs, and ignore all terrain. combined with Pressurized Glands, these units can fight almost anything. 

However, the Creeper strain, allows for teleportation between any two pieces of creep. While this may not seen like much, the first Korhal mission, which happens very shortly after making this choice, you have to defend siege turrets that are falling out of the sky, and are scattered all over the map. Because they generate creep, the Creeper strain can move between them far more quickly than any other unit, and really have a chance to shine. So it works either way.

The Mutalisk is the only unit where two of the possible mutations cannot both happen at the same time.

1. Vicious Glave doubles the numbers of bounces and increases the damage of each bounce.
2. Rapid regeneration allows your mutas to heal 10 hps a second after spending 5 seconds out of combat.
3. Sundering Glave removes the bounce and give a +9 damage bonus against armor.

This unit's evolution is simpler than it appears. you choose between having a muta evolve into a Brood Lord, or into a Viper. The Viper in the campaign has an anti-air, anti-armor attack, in addition to its spells and is the closest thing the Zerg have to an anti-air only fighter. 

Both the Viper and the Brood Lord have the same purpose, although they go about different ways. They exist to siege enemy bases from the air. The Viper does it by pulling powerful units out from behind the wall and by reducing the range of defenders to 0.5, as well as providing some counter to an air response. They help your ground forces get into the base without suffering to many losses. The Brood Lord does it by sending down an endless stream of broodlings and heavy bombing, reducing defenses to dust without ever coming in range.They need anti-air support, but nothing else to destroy a base. I don't have an opinion on which one you should choose.

The Ultralisk has two types of abilities: survival and AoE.

1. Burrow Charge allows your Ultralisks to quickly get into melee range, also stunning all units near where they surface, giving you the in game equivilant of the advantage of surprise. (I found that the unit blockage that this mutation was meant to overcome no longer exists, making it moot.)
2. Tissue Assimilation gives you a 40% lifesteal, greatly increasing survivability.
3. Monarch Blades makes splash damage equal base damage, a massive AoE increase. (This is the best choice for unmodified Ultralisks)

The evolution is a choice between the Noxious Strain and the Torrasque Strain.The Noxious Strain does a constant 5 damage per second to all enemy units within melee range, and has an ability with a 10 second cooldown that deals 20 splash damage to the target, and can be put on auto-cast. The Torrasque Strain enters a 200 health cocoon for a short time when it dies, before emerging with full health. This can only once a minute. 

If you pick the Noxious Strain, your splash damage will be high enough that you can pick Tissue Assimilation to increase tanking effectiveness. If you take the Torrasque Strain, it will be almost impossible for you to lose an Ultralisk, and monarch blades will bring it's damage up to match. If, however, you want to max damage or survivability, you can switch it around.

I have nothing to say about the missions, as there are many ways to win, and I can't describe them all. Just go to Char first, than in order of appearance.