Warmachine armies rely heavily on their warcasters. A Warcaster's abilities, spell list, and feat determine how they support their warjacks and troops, so two armies lead by two different warcasters (even different versions of the same warcaster!) will function differently even when the armies are exactly the same.
This article breaks down warcasters according to their main gameplay mechanics.
Shoot Them With Guns

Cygnar is the army you want if you want specialty 'jacks with guns. However, how a warcaster utilizes those guns differs from 'caster to 'caster.
Siege is made to crack armor at a distance.
He can hit multiple targets with his ground pounder or a single target with his Rocket Cannon, remove the Stealth Ability with the Mage Sight Spell, protect his own troops or open lines of sight with the Foxhole Spell, and, most importantly, he can drop enemy ARM the first time with the Breach Feat.
The Defender Warjack gives Siege the Firepower he craves.
Expanding with Siege Brisbane.
Lieutenant Caine is a hit and run infantry killer.
He can cast the Snipe Spell to increase the RNG of someone's guns (especially his own), the Deadeye Spell makes utility shooters like Arcane Tempest Gun Mages deadly accurate, his SPD gets him close enough to shoot things before he casts the Teleport Spell to get away, and his Maelstrom Feat owns every single single wound enemy infantry model on the table.
Caine needs a 'jack to help him crack armor, like the Ironclad Warjack or a Stormclad Warjack. Your choice of target for Deadeye and Snipe will depend on how much work you need Caine to do, but Arcane Tempest Gun Mages are good for Deadeye, and with the Gun Mage Officer they can even help support more 'jacks in a Caine army.
Expanding with Lieutenant Caine
Captain Sloan is a ranged assassin.
Her rifle has the Weapon Master Ability, and she can shoot at targets from up to 16" away. The Fire Group Spell increases the range of her battlegroup, the Refuge Spell mobilizes her 'jacks to shoot and move to protect her, Deadeye increases the accuracy of anything else she needs to shoot, and the Firing Squad Feat not only generates extra shots for herself and her 'jacks, but it increases the ranged accuracy of everything in her army.
Her spells and feat favor at least one Defender Warjack and maybe one Hunter Warjack in her army. A Trencher Commandos Unit with Scattergunners and/or Arcane Tempest Gun Mages Unit really benefit from her feat and deadeye.
Expanding with Kara Sloan
War of Attrition

Cygnar's Attrition options are somewhat odd, given that their army is often made up of costly troops and 'jacks that incorporate both melee and ranged weapons, so it takes particular warcasters to create attrition-based lists.
Constance Blaize leads melee infantry to battle.
She protects them with her Banishing Ward Spell, and enhances their charge range with the Crusader's Call Spell. When she uses her Divine Intervention Feat, slain friendly faction models give her focus and extra ARM, and the following turn she throws all of it back at the enemy through the Transference Spell as her remaining troops spend her focus to boost their attack and damage rolls. At some point, she may make use of the Flashing Blade Spell and her Reach weapon to attack multiple models for the cost of a single focus point, and woe to the model standing in range of one of her Morrowan Knights, as she gains the Flank Ability from their presence.
Her special abilities go to the character Gallant Warjack and the Morrowan Precursor Knights Unit. In addition, cheap melee infantry in the form of a Sword Knights Unit can help power her feat while specialty melee infantry in the form of a Storm Blades Unit can lead the counter-assault.
Expanding with Constance Blaize
Captain Darius fixes and tunes warjacks for the long haul.
The Fortify Spell keeps them standing and protects them from damage, and then he can throw them at the enemy with the help of his Crane and his Full Throttle Spell letting them charge for free and swing with boosted melee attacks. In addition, he and his half-jacks can repair the 'jacks, and after the army has been pounded he uses his Pit Stop Feat to fully repair those 'jacks he and his half-jacks can reach, bringing them back to prime condition.
For Darius, nothing less than three heavy warjacks will do. If you plan to utilize warjacks with Reach, you can support them with cheap Sword Knights Units for the Flank Ability to increase their damage.
Expanding with Captain Darius
Warjack Power

These warcasters rely on warjacks to deal the majority of their damage. Again, the number of warcasters under this category speaks to the variety in gameplay.
Commander Nemo (aka "The Old Man") uses magic to enhance a single 'jack in his battlegroup and shuts down enemy warjacks hard.
Models increase Nemo's focus through his Arcane Accumulator. He in turn Supercharges one of his 'jacks to give it up to five focus, casts the Disruption Field Spell to make it stronger and disrupt enemy warjacks, and then he casts the Locomotion Spell to move it around before it gets just the right angle from which it can pound/shoot things to death. When faced with enemy warjacks, Nemo's feat can disrupt and damage them, and the Voltaic Snare Spell can lock them down in place.
Nemo doesn't wait for other people to cast spells for his accumulator, so he might include Captain Strangewayes, Journeyman Warcaster , or the Lady Aiyana and Master Holt Unit to fuel his focus. And while a Lancer Warjack gets his spells out onto the table, what he really needs is a big 'jack to feed like the Thunderhead Warjack.
Expanding with Commander Nemo
General Nemo runs multiple 'jacks and fuels them up for a massive feat turn.
The General is a massive upkeep resource hog, putting the Polarity Shield Spell on a frontline unit or 'jack to prevent charges, the Lightning Shroud Spell on a 'jack to make it stronger and deal with nearby infantry, and the [[Fail Safe Spell on a 'jack specifically positioned to take hits (it will ignore lost systems and gains an ARM bonus). When he uses his High Voltage Feat, ALL his warjacks get full focus, at which point he casts the Energizer Spell to move ALL of them up to 3" before they go to town.
A Squire Solo helps the General fuel his upkeeps and battlegroup, while various combinations of warjacks serve him well. In addition to the Thunderhead Warjack, Nemo can get the most out of 'jacks that can use extra movement and benefit from a full focus feat turn, like the Hammersmith Warjack (or any melee warjack, for that matter) or the Charger Warjack
Expanding with General Nemo
Captain Kraye turns his battlegroup into a hit and run warjack force.
Kraye's battlegroup functions like cavalry, with all the light warjacks gaining the light cavalry rules. He puts the Full Tilt Spell on a heavy warjack to double its SPD at the cost of ranged attacks, and casts the Guided Fire Spell to benefit all the 'ranged 'jacks in the list. If difficult terrain presents itself, the Easy Rider Spell gets the 'jacks through. Then when he puts up the Horsepower Feat, his Full Tilted heavy charges at base SPD *2 + 5". Even a SPD 4 'jack charges 13" this way. And all those melee attack rolls? Boosted for free.
The Hammersmith Warjack or Centurion Warjack can really benefit from Full Tilt, while a Hunter Warjack and/or a Cyclone Warjack put the shots out from Guided Fire.
Expanding with Captain Kraye
Army Support

Some 'casters seem designed to stay at the back of their army and literally support them with spells, upkeeps and feats. If these 'casters get anywhere near the enemy, something is going to go wrong.
Haley supports her army by debuffing the enemy and generating attacks for her army.
She can improve armor with the Arcane Shield Spell and increase ranged accuracy by casting Deadeye. Then she gets close enough with her control area, drops the Temporal Barrier Spell to slow the enemy army advance and hit it easier with her own. Finally, her Blitz Feat gives her army an extra attack for each model, potentially hitting whatever she wants them to with the help of Temporal Barrier and/or Deadeye.
Haley likes a Squire Solo to increase the RNG of her Temporal Barrier. After that, a lot of is simply choosing models. While she can turtle behind her Temporal Barrier and defensive and ranged models, she can also support a close combat oriented army by preventing counter-charges with Temporal Barrier and gaining a speed/pacing advantage over other armies.
Expanding with Captain Haley
Stryker directly supports his army with spell buffs and an attrition based feat, outfighting and outlasting enemy armies.
He wins the ranged game by putting Snipe on a unit and the Blur Spell on another and Arcane Shield on something big and heavy like a warjack. Enemies will be outranged unless they can ignore/bypass/punish those three buffs. On top of that, he can drop an Earthquake Spell to create lines of sight or attack opportunities, and when he needs it most, he can boost his army's armor with his Invincibility Feat to survive freestrikes, alpha strikes, and counter-assaults.
Ol' Rowdy Warjack is a good starting point for a melee warjack, though a Stormclad Warjack gives you the advantage of a Reach weapon and focus efficiency with a Stormblades Unit. Options for the Snipe include a Defender Warjack or a Longgunners Unit. High armor models are choice to benefit the most from the feat.
Expanding with Commander Stryker
Warcaster Assassins

Even though every warcaster can pull off assassinations with the right application of focus, support and luck, when these warcasters get into combat they play for keeps.
Lord Commander Stryker (aka Darth Stryker) waits for his moment, gets in close, powers up his suit and swings at stuff until they die.
Stryker supports a melee army by protecting them with the Deflection Spell and casting the Positive Charge Spell on a Reach 'jack to give his melee troops additional hitting power. Then if there's any opening at all, he overcharges his suit, takes damage, casts the Velocity Spell to position himself and charges whatever needs to die. If he fails he can always use the Rolling Thunder Feat to get one last chance to finish off his target.
Ol' Rowdy Warjack is a solid first choice for Stryker. His affinity with the 'jack supports his playstyle perfectly. A Sword Knights Unit with flank from a Reach 'jack is a good second choice (possibly a Lancer Warjack or Stormclad Warjack).
Expanding with Lord Commander Stryker
Captain Caine turns his guns into melee weapons, crashes in on his target and shoots them in the face until they die.
The definitive change to Caine from his prime version is his ability to shoot in melee combat with the Gunfighter Ability and his ability to teleport via the Gatecrasher Spell into combat and shoot someone in the face. What makes it viable as a kill method is his abnormally high ranged accuracy (which he uses even in combat) and the Overpower Feat that increases the damage of his guns with every shot. And Caine can shoot until he's out of focus.
Caine needs as much focus and shots to power his feat as he can get, so a list for him often starts with the mercenary Reinholdt, Gobber Speculator Solo and a Squire Solo. After that he can be used to power a Defender Warjack for two focus every turn until the feat, or he can use his precious focus to enhance a ranged model/unit's accuracy with the Deadeye spell.
Expanding with Captain Caine
The epic form of Victoria Haley holds you down with magic and her feat until she lines up the perfect opportunity to set up the kill.
Haley speeds up parts of her army with the Temporal Acceleration Spell and protects them with the Deceleration Spell. When she needs to set things up for the kill, she activates her Temporal Shift Feat or throws the Time Bomb Spell around to de-buff things. Finally, her killstroke isn't a direct spell to the face, but rather a casting of the Telekinesis Spell that opens up an assassination line on the enemy commander.
Good places to start with epic Haley is to get a Squire Solo to extend the range of her denial based feat, pick up some kind of heavy warjack to benefit from her Warjack Bond Ability, and bring along the Thorn Warjack Character to get her spells where she needs them to go.
Expanding with Major Haley