I can think of 4 good candidates for the death knight hero: Thassarian, Darion Mograine, Teron Gorefiend, and Koltira Deathweaver. While Teron Gorefiend might be the most universally well know, he's also technically an "old school" death knight, from a different generation that isn't even Scourge-aligned. With that in mind, I'd go for Thassarian as the death knight hero. He's possibly the most developed of the new batch of death knight NPCs, and his story of rescuing Koltira is one of the biggest dangling plot threads in the WoW story right now.
The hero ability is another question. Perhaps the most obvious ability would be to let the death knight summon a 1/1 ghoul, but that might overlap with the paladin ability. Another interesting twist could be to give the death knight a Death Coil ability that does either 1 damage to an enemy or 2 healing to an allied undead minion.
So for spell cards, I figure death knights would be all about their iconic moves, focusing on minor AoE and some healing.
Death and Decay - The standard field clearer, doing 1 damage to all minions.
Death Strike - This strike would come with a blood shield effect of sorts, doing 2 damage and healing 2 damage and adding 3 armor to the hero.
Outbreak - At the start of your next turn, deal 2 damage to target minion. Lasts 3 turns.
Heart Strike - deals 2 damage each to up to 3 adjacent minions.
Death Pact - destroy a targeted friendly minion. Heal yourself for that minion's defense total.
Death Siphon - deal 3 damage to an enemy and heal 5 damage to yourself.
Remorseless Winter - Freeze all minions.
Plague Leech - Discard a card. Gain 2 mana for this turn only.
Dark Transformation - An undead minion gains +4/4.
Leap - An undead minion gains Charge.
Strangulate - Silences a minion
Runeblades and minions
The Runeblade is one of the more iconic parts of the modern death knight, so you would, of course, be able to grab a few of those. The Greatsword of the Ebon Blade would be the basic free blade. Probably a 2/2. But we could also, for example, get a few legendary runeblades in there. A Corrupted Ashbringer could be a legendary level Runeblade, say, at 5/3, but with the downside of damaging the death knight every time they use it. We could also get access to Shadowmourne, which gives +1 attack every time you attack with it (mirroring the Soul Fragment mechanic in game). I'd also kind of like to see Bryntroll, the Bone Arbiter in there, healing +1 every time you attack with it. It's a pretty solidly iconic weapon from ICC.
Death knight minions would definitely be focused on the undead, and you could probably make them their own class, much like beasts.
Banshee - Battlecry: Silence.
Wailing Banshee - Death Rattle: Possesses random enemy minion, converting it to your side.
Unstable Abomination - Taunt. Death Rattle: Explodes, dealing 3 damage to 2 enemy minions.
Army of the Dead - Summon 3 1/1 ghouls. Also, 2 random undead minions from your deck will transfer to your hand.
Ebon Blade Initiate - Battlecry: Summons 2/1 ghoul minion.
Cult of the Damned Necromancer - summons a 1/1 ghoul whenever a minion dies.
Raise Undead - Summons a ghoul that has charge and power and defense equal to the number of undead minions already killed in the game thus far.
Lord Marrowgar - This would be one of our legendary cards. Battlecry: does 2 damage to all minions ala Bonestorm. Also has Windfury ala Bone Slice.
Of course, all of the above is just using mostly arbitrary numbers, but I figure if a Mage can throw a 10 damage Pyroblast at me, or a warrior can play a couple Shield Block cards, it can't be that bad to throw out a few death strike cards. I see death knights as being that annoying deck that has way too many minions to deal with and backs it up with enough self-healing to be truly annoying. Of course, however they do it, I just want to play my favorite class in Hearthstone. Maybe we'll get a Hearthstone expansion by next BlizzCon, right?
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.