Here’s what we know so far, feel free to jump into the comments to add anything!
 30 cards
 18 specials and 12 “basic” is the standard setup, with basics defined as ANY/ANY cards with typically lower attack values (though MOMENTOUS SHIFT is A3 that can power up) and basic effects that are not deckdependent, such as moving or drawing cards.
 Robin Hood has 16 specials and 14 basics.
 Sinbad has 17 and 13.
 InGen has 21 and 9.
 The Raptors have 24 and 6.
 Dracula and Dr. Jekyll both have 22 and 8.
 Invisible Man has 21 and 9 (or arguably, 30 and 0).
 Sherlock Holmes has 23 and 7.
If you’re building your first Unmatched deck, I would stick to an 18 and 12 structure or at least close to it. You can always tweak from there.
Special cards for Heroes and sidekicks:

 Specials are split between the Hero and the sidekicks, except in the cases of Bruce Lee, the Raptors and the Invisible Man, who can use all 30 of their cards. Dr. Jekyll & Mr. Hyde are only one character but he can’t access cards of his other personality.
 In terms of card counts for sidekicks, it makes no difference if the sidekick is a single personality, like Merlin or Porter, or a set of sidekicks, like Medusa’s Harpies or Robin Hood’s Outlaws.
 So far, Dracula’s Sisters have the most cards among sidekicks at 8, followed by Merlin at 7.
 Porter has the fewest cards among sidekicks, at 3 cards.
Special card mix:

 Every Hero has a “bread and butter,” which is at least 3 copies of one card and sometimes 4. This is typically an attack, but not always. There can be more than one. Dracula is an exception, with many sets of 2 attacks but no set of 3.
 Every sidekick set has a bread and butter with 2 copies of at least one card.
 Arthur/Merlin has 11 different special cards, which appears to be the most for a standard deck setup. Bruce Lee has 13, though if you consider his 6 JEET KUNE DO cards to be variations of the same card, then he has only 8.
 Every deck has a mix of combat cards and scheme cards. Note that in Epic Duels, there were characters with only combat cards, like Darth Maul, and characters with only special cards (essentially the same as scheme cards) like Emperor Palpatine. There are only 12 cards in Epic Duels but I think it’s possible to have combatonly or schemeonly in Unmatched.
 Every deck has power attack cards, or attack cards without a defense value.
 Not every deck has power defense cards. Sinbad doesn’t.
 Attack values: So far, A6 is the highest unmodified attack value, which appears in several decks.
 Defense values: D4 is the highest defense value I’ve found so far for a hero, but note that Merlin does have 2x DAll cards.
 So far, I’m not seeing any card do more than 2 direct damage, though I don’t think 3 direct damage would be overpowered. However, I don’t see 4direct damage cards like we do in Epic Duels, like THROW DEBRIS, THERMAL DETONATOR or WHIRLWIND ATTACK as part of Unmatched. They aren’t so far, anyways, and I think 4 damage (at least without conditions) would be overpowered.
 Alice’s LOOKING GLASS card establishes that you can have quite a few effects in a single card — 3 in the case of that card, from a set of 4 possibilities. This goes beyond Epic Duels, which typically only had 2 effects in a single card, though fans often expanded it to 3 effects.
 Just note that a lot of decks have 3 copies of FEINT and it is typically the backbone of your defense with its secondaryeffectcanceling ability. This means that higher attack values matter more in Unmatched, and secondary effects matter a little less because you could always run into a FEINT.
Special card counts:
Alice (8 cards, 14 total): 3, 2, 2, 2, 2, 1, 1, 1
Jabberwock (2 cards, 4 total): 2, 2
Total: 10/18
King Arthur (6 cards, 9 total): 3, 2, 1, 1, 1, 1
Merlin (5 cards, 7 total): 2, 2, 1, 1, 1
Any (1 card, 2 total): 2
Total: 12/18
Medusa (4 cards, 11 total): 3, 3, 3, 2
Harpies (2 cards, 5 total): 3, 2
Any (1 card, 2 total): 2
Total: 7/18
Sinbad (3 cards including one with 7 variations, 13 total): 4, 2, 7
Porter (1 card, 3 total): 3
Any (1 card, 1 total): 1
Total: 5(9)/17
Big Foot (3 cards, 8 total): 3, 3, 2
Jackalope (1 card, 3 total): 3
Any (3 cards, 7 total): 3, 2, 2
Total: 7/18
Robin Hood (4 cards, 10 total): 3, 3, 2, 2
Outlaws (1 card, 4 total): 4
Any (1 card, 2 total): 2
Total: 7/16
Bruce Lee (8 cards including one with 6 variations, 18 total): 4, 2, 2, 1, 1, 1, 1, 6
Total: 8(13)/18
Raptors: 4, 3, 3, 2, 2, 2, 2, 2 with only 6 basic cards.
Total: 8/24
In Gen: 4, 3, 3, 3, 2, 2, 2, 2 with only 9 basic cards
Total: 8/21
Basic cards:

 Basics are typically 12 card sets but there are decks with more (Sinbad and perhaps Robin Hood) and many with less..
 All are ANY/ANY (A/A) cards that can be used for any character in the set, and for either attack or defense. Obviously for single character decks like Bruce Lee and Invisible Man, they are only for that one character, but even for Invisible Man you can see which of these cards stands out.
 They’ll come in sets of 2 or 3, but usually 3.
 A/A values range from 14 but tend to be on the low side like 1 or 2.
 Unlike Epic Duels, the attack and defense values are always the same. There’s never more than 1 value per card, never different attack and defense values like an A4D1 or A1D2, at least not so far.
 FEINT appears 3 times in most decks but some don’t include it.
 REGROUP appears 3 times in most decks but again, some don’t include it.
Here is a list of some of the more common basic cards so far:
FEINT
A/A 2. IMMEDIATELY: Cancel all effects on your opponent’s card.
BOOST: 2; but it’s only 1 in the Arthur and Sinbad decks
Appears 3x in every deck so far: Arthur, Alice, Medusa, Sinbad, Big Foot, Robin Hood, Bruce Lee
REGROUP
A/A 1. AFTER COMBAT: Draw 1 card. If you won the combat, draw 2 cards instead.
BOOST: 2; but it’s only 1 in the Arthur and Sinbad decks
Appears 3x in every deck so far: Arthur, Alice, Medusa, Sinbad, Big Foot, Robin Hood, Bruce Lee
MOMENTOUS SHIFT
A/A 3. DURING COMBAT: If your fighter started this turn in a different space, this card’s value is 5 instead.
BOOST: 1
Appears 3x in: Arthur, Sinbad, Big Foot, Bruce Lee and 2x in Alice
SKIRMISH
A/A 4. AFTER COMBAT: If you won the combat, choose one of the fighters in the combat and move them up to 2 spaces.
BOOST: 1
Appears 3x in: Arthur, Big Foot, Bruce Lee and 2x in Alice
EXPLOIT
A/A 4. AFTER COMBAT: Draw 1 card.
BOOST: 1
Appears 2x in: Sinbad
MAXNOME FOE
A/A 3. DURING COMBAT: Discard the top card of your deck. Add its BOOST value to this card’s value.
BOOST: 2
Appears 2x in: Alice
LEAP AWAY
A/A 4. AFTER COMBAT: If you won the combat, choose on of the fighters in the combat and move them up to 4 spaces.
BOOST: 1
Appears 2x in: InGen and Sinbad, appears to replace SKIRMISH
DASH
A/A 3. AFTER COMBAT: Move your fighter up to 3 spaces.
BOOST: 1
Appears 3x in: Medusa
SNIPE
A/A 3. AFTER COMBAT: Draw 1 card.
BOOST: 1
Appears 3x in: Medusa
WILY FIGHTING
A/A 3. AFTER COMBAT: Deal 1 damage to each opposing fighter adjacent to your fighter.
BOOST: 1
Appears 3x in: Robin Hood
SNARK
A/A 3. AFTER COMBAT: If your fighter is adjacent to the opposing fighter, draw 1 card
BOOST: 1
Appears 3x in: Robin Hood
Arthur, Big Foot and Bruce Lee all have the exact same basic deck with 3 each of FEINT, REGROUP, MOMENTOUS SHIFT and SKIRMISH.
Alice has a similar deck, but has a 33222 structure, giving up 1 each of MOMENTOUS SHIFT and SKIRMISH to include 2 MAXNOME FOE. So far Alice’s is the only deck to include MAXNOME FOE and it’s possible that it is her card only, but I don’t see why you couldn’t use it, 2 or even 3 copies, in any other basic deck. It is a pretty good card IMO.
Sinbad has a similar deck as well, despite the unique structure of having 13 basic cards instead of 12. He has 3 copies of FEINT, REGROUP and MOMENTOUS SHIFT just like the Arthur/Big Foot/Bruce Lee deck. Then, instead of 3 copies of SKIRMISH, he has 2 copies of LEAP AWAY, which is essentially a slightly stronger version of the same card, and 2 copies of EXPLOIT. Like Alice’s deck with MAXNOME FOE, so far Sinbad’s is the only deck to include EXPLOIT and it’s possible that it is his card only, but I don’t see why you couldn’t use it, 2 or even 3 copies, in any other basic deck. It is a pretty weak card IMO. He’s also the only one with LEAP AWAY but I already have plans to give it to others.
Medusa and Robin Hood both have unique decks, which I find interesting. As they are the only 2 ranged Heroes, it makes sense to me that they wouldn’t have the same basic cards as the other decks — MOMENTOUS SHIFT especially makes less sense in a ranged deck. However, I would think they’d have the exact same basic deck as one another, the default “ranged” deck. I mean, of 5 melee characters, 3 have the exact same deck, and the other 2 have slight variations of that deck.
Medusa and Robin Hood, meanwhile, both share the 3 copies of FEINT and REGROUP like every basic deck does, but Robin Hood appears to have 9 more basic cards that he and his Outlaws share while Medusa has only the standard 6 more basic cards.
InGen throws another wrinkle into it. It also has 3 copies of FEINT and REGROUP but only 3 more basic cards in total. I don’t see why SNIPE couldn’t be in 2 or 3 of these 3 decks, but it isn’t.
Raptors have an altogether unique deck and as they have a unique situation with 3 indiscernible characters it makes sense that they would have a unique deck. I think it goes to show that now that we kind of know how the box is established, we can go ahead and think outside of it. The Raptors only have 6 basic cards but I wouldn’t necessarily try that for another deck since theirs is so unique.
The Cobble & Fog set adds some additional interesting basics:
Sherlock’s STUDYING METHODS is clearly his card, but I think the same card and effect could be used by another insightful character with a different title. His EDUCATION NEVER ENDS card is a twist on REGROUP.
Dr. Jekyll & Mr. Hyde have an interesting card called DUALITY OF MAN but it couldn’t possibly be used for any other deck.
Invisible Man sort of has his own set of “basics” but they interact with his Fog tokens and are uniquely his.
Some tips on making your own deck:
I’ve written at length about how to make Epic Duels decks, so I would start there because the concepts are all the same: You need to figure out what your hero does to win the game, and how a unique combination of cards helps him do that.
My best advice is to start out trying something conventional, then break the rules carefully, and one at a time. So for conventional, get a hero with either 1 tough sidekick or a group of 34 weak ones. Go with 18 “special” cards and make sure you’re at least giving your sidekicks 3 of them, but more if you want to.
In terms of setting up your cards, if you’re going for a melee hero, I would default to the Arthur/Big Foot/Bruce Lee deck unless you had some specific reasons to include another card the way Alice or Sinbad do. In creating a ranged deck, I would start with the 12card Medusa deck. You could swap out DASH and/or SNIPE with SNARK and/or AMBUSH and/or WILY FIGHTING.
So that leaves you with at least:
 1015 cards for your hero
 34 “bread and butter” cards, probably an attack card
 at least one other combo of 45 cards that can give you a good turn or an advantage
 36 cards for your sidekicks, with at least 23 “bread and butter” offense cards
 12 “basic” any/any cards
 make sure there are some Scheme cards in there, or add them now
The effect of Manxome Foe may be reused by other cards, but the card itself is definitely Alice specific as the name of it comes from “Jabberwocky.”
Thanks for the clarification Josh!
My brother keeps declaring when he defends with ‘momentous shift’ that he moved on his turn so his defense is a 5. Is this right? Or is he cheating?
I see how he could interpret the card that way, but I really don’t think he’s right. I think “this turn” is your opponent’s turn when you’re on defense, and he almost for sure didn’t move on that turn, right? If he moved on his turn, that was last turn. He could move on his turn and then use MOMENTOUS SHIFT as an A5, but once his turn is over, the movement doesn’t still count.
You could ask at boardgamegeek for an official answer but I’m pretty sure that’s the one you’re going to get.