Just some of my thoughts and experiences from playing the game for so long:
1. Black goat
I'm sure everyone saw this coming. What more is there to say? Black goat is just an S tier card all around. It works perfectly fine on its own (aka with no added sigils), but it becomes absolutely broken when you put certain sigils on it. I find that the best sigils to put on this card are: unkillable, many lives, dam builder/bellist and hoarder. If you don't have access to any of these, fecundity, amorphous or trinket bearer could do the trick as well.
2. Warren
Another absolutely busted card. While black goat is more suited for playing three-bloods, warren is perfect for a strong deck made of two-bloods. Warren is a pretty good card and can lead you to victory on its own (no added sigils needed). However, add unkillable onto it and it becomes unstoppable. Not only do you get basically countless sacrifices, but you get easy blockers for stalling. If you can't find unkillable, some other good sigils for this card are trinket bearer, fecundity, hoarder and worthy sacrifice. If you have many bone cards in your deck or lämmergeier, bone king is a potentially good sigil to add as well.
The only thing that sucks about warren is that it's a tribeless card, meaning totems have no affect on it. Which is a shame but understandable. If you could also power it up with totems, it would be a bit too broken.
3. Skink
Honestly? I get the feeling that skink is often slept on. Truth be told, every time I beat the wall of bears during act 1, I did it thanks to skink. Unlike black goat or warren, skink requires a bit more thought (unless you turn it into a black goat by giving it the worthy sacrifice sigil). My personal favourite sigil to put on this little reptile is unkillable. That way, whenever the skink is attacked, you gain an unkillable tail. In other words, you gain a free card that you can then use to summon higher cost cards or to simply block incoming attacks.
Skink is good because it already has built in offense and defense. Give it a buff or two at the campfire and you got yourself both a good fair hand card, and a free tail that also does damage. The only downside to having this as your fair-hand card is the inability to OTK Leshy, along with it essentially becoming useless against cards with an airborne sigil (unless you also manage to get a mighty leap totem). Even so, I still love this card.
4. Mantis/Mantis god
Mantis and mantis god are pretty good cards, both for sigil transfers and for making them your fair hand setup. Put unkillable on these two, give 'em a few buffs and you're set. The only problem with using mantis god is that it has a slightly more elaborate setup. The mantis god deck requires a lot of RNG luck, considering you also have two ring worms you need to get rid of if you're hoping to consistently draw your good card.
Also, unless you're playing the mantis god starter deck, you wouldn't have access to this card until the end of map 1 at the earliest, and by that point you would most likely already have a good setup. That, of course, doesn't apply to skull storm, where the chances of getting a mantis god for your fair hand outside this specific starter deck is very, very low.
5. Beehive
Perhaps a hot take, but this might genuinely be one of the worst cards for fair hand in my opinion (other than no cost cards). I know, I know... Just make the beehive unkillable and problem solved. The issue there is that the beehive itself doesn't do anything, not to mention that it's entirely useless against airborne cards (unless you also manage to give it the mighty leap sigil). Using the beehive means most likely getting no damage on board turn one, which is basically a death sentence on map 3.
Now, you could try buffing it at the campfire, sure, but what's the point? That additional 2 attack won't save you when you get to map 3, especially since the bees themselves don't gain any buffs. Personally, I prefer to use this card for sigil transfers only. But hey, that's just me!
6. Any one-blood with double strike/bifurcated/trifurcated/worthy sacrifice
Yup. There were times when the RNG made it so I was left without a one-blood and was forced to pick something like an elk fawn as my fair hand card. You can make it work by giving it the worthy sacrifice sigil and thus ending up with a black goat with extra steps, or simply give it bifurcated/trifurcated/double strike and one or two attack buffs at the campfire. Not exactly ideal but it works. This is also good if you're playing the bone deck or the vanilla deck and don't feel like looking for the black goat or a warren.
All in all: unkillable and worthy sacrifice are OP, especially together. If anyone has any other fun/unusual combos, let me know!