"Those Cards"

Temperance
5 disks
Ace of cups
Knight of Swords
Hierophant
4 of Wands
9 of Wands
Empress and Emperor

If they work for me, usually the whole deck works for me. There may be some more, but these are cards I always notice.

I'm usually pretty easy with decks, it takes a lot to turn me off a particular deck but cards I do look at are:

The Moon
The Empress

I have to like the Moon, it's a deal breaker for me if I don't.

High Priestess
Judgement
The Moon
Temperance
Strength
Knight of Wands
Queen of Cups
Knight of Sword
Aces, 7s

plus minors have to be illustrated...

Besides the aforementioned Strength, I also have to like the Moon and Temperance to really love a deck. And there's the Fool. I rarely really love a Fool card, but some depictions turn me right off. Any Fool dressed as a clown is a big NOPE. I'd also prefer they not be dressed as court jesters, but that rules out so many decks...

Interesting question!

The first one has to be The Star, if the depiction is very good, almost take me 50% chance to grab the deck,

Two of Cups, in salmon pink color or at least filled one of the attributes in the cards, the mos t lovely scene in the deck.

Or is it just me who craves for not hopeless in love? LOL #stolenconfession.

The last options are The Strength, Death, The World, Court cards

High priestess
Death
Devil
Moon
Two of cups
Three of swords
Aces
Those are the first ones I look at and need to feel some connection with at least.

Funny to see some cards mentioned a lot ahah

For me it is :

The Hermit
The Magician
The King of cups

And I'm generaly curious about The Devil, The Lovers and the Aces.

One deck that I find incredible but The Devil had tempered my enthousiasm is the Slow Roller Deck. I find that Devil card a bit "grotesque"... :'(

I'm still very much a beginner, so I haven't got any hard and fast requirements as yet, but this is certainly worth thinking about (though I'm trying not to buy any more decks for a good long while).

One card I'm often drawn to is the Two of Swords (especially the Morgan Greer version, and the classic RWS - I also rather like the Fey Tarot one and the Wildwood "two of arrows" is pretty stunning).
The Tower seems to be a fairly important card for me. One of my favourite cards in the Green Witch Tarot is the "Wild Hunt" card which is pretty much the Tower in her system. It just looks kind of epic, plus the tower in the picture reminds me of a tower in Skyrim which kinda works well thematically (but I won't bore on about that any more!)
I don't necessarily need a GOOD Magician, but it's an easy card to get badly wrong - I really like the overall style of the Hanson-Roberts Tarot, but oh that Magician - goofy Fabio... (With apologies to any fans of this particular card!)
The "heavenly bodies" cards - star/moon/sun - are all ones I usually look at (the Pole Star from Wildwood... gorgeous!)

All 4 Queens

I prefer that the 10 of Pentacles and 10 of Cups not portray families. This is not a hard requirement but a strong preference. I don't like it when the 4 of Pentacles (or whatever the earth suite is) is judgmental and about greed. I see it as a more neutral card about security and would rather not have it overinterpreted in the illustration.

The Moon, The Devil, The Lovers and The Star are some of the first cards I look at when considering a deck but the overall way the deck uses imagery is more important.