If you had the option to choose your inital 4 card hand, what would you take? Obviously there isn't a "one size fits all", as different villains call for different tools, so feel free to be creative with it.
I'll start with what one of the easier characters for such a list.
Waith: 2 Impromptu Inventions, Grappling Hook, MicroTargeting Computer: This pretty much gives you a complete first turn damage setup with a Grappling Hook as safety net. I'd take this hand vs any boss, any day.
Mr. Fixer: Driving Mantis, Dual Crowbars, Overdrive, Toolbox.
Slightly on the offense side, being able to deal either 1 target 4 damage or 2 targets 2 damage. Yets still able to toss some environment/villain damage on occasion for some protection. Early overdrive to ensure that Salvage Yard will be able to retrieve one. Toolbox to give the extra cards to get Charge/Overdrive/Bloody Knuckles or replacement tools or styles if needed.
This gets both modules and some other useful stuff into your hand in addition to thinning out your deck, all on the first turn. And who doesn't love a first-turn Impale?*
The Visionary: Wrest the Mind, Twist the Ether, Precognition, Suggestion.
Nightmist: Amulet of the Elder Gods, Mistform, Call Forth, anything with a {4}.
Darkwatch Nightmist: Enlightenment, Master of Magic, Starshield Necklace, Tome of Elder Magic.
Bunker: If I care only about winning, Flak Cannon, Grenade Launcher, Heavy Plating, Turret Mode. If I don't want to be completely bored, these cards are at the bottom of my deck (except the Plating), and I do something like Omni-Cannon, Gatling Gun, Ammo Drop, and AuxPS, drawing DecommWare on my first Initialize.
Oh gawd, I get that all the gorram time. No thanks!
Ra: Imbued Fire, Flesh of the Sun God, Drawn to the Flame, Flame Blast
Dude, it's the best. You get 4 staves, PLUS an entire other 4-card hand to pick from. After that it doesn't really matter what other cards you get, they pretty much all do fire.
Fanatic: Brutal Censure, Final Dive, Aegis of Resurrection, Wrathful Retribution
Redeemer Fanatic: Absolution, Smite the Transgressor, Divine Focus, Prayer of Desperation.
Prime Wardens Fanatic (assuming she turns out as we've heard she will): Sacrosanct Martyr, Embolden, Chastize, Holy Nova.
I hate the redundancy of drawing multiple Staffs and being forced to destroy them. It's sometimes worth it for the healing or the extra 1 damage (or if you draw Flame Spike), but overall I'd rather do more interesting things.
Does she have three, or four? I started with three once - sadly the fourth card was an Inventory Barrage, not really of much use at the start of the game. But that was a pretty epic first turn, anyway :).
She only has three, Tesla. Very few heroes have 4 copies of one card in their deck. The only one I can think of at the moment is Ra's Staff. A card as powerful as Impromptu isn't going to have more than 3 copies. Though if there 4 copies, it would be the best starting hand, since on top of putting equipment into play, you'd get several free draws and end up with one free play.
Omnix has 4x Reset, and if you think it can't be a powerful card, Argent Adept has 4x Arcane Cadence and Nightmist has 4x Oblivion. Ab'Zero is probably the only hero who has two x4s, though (both his Modules).
Apart from Wrathful Retribution and the Adept's instruments, are there any hero cards of which there is only one copy? Not counting Nightmist's cards with their differing numbers as the text and card names are the same. I can't think of any, off the top of my head...