Four reviews for Joe and none for Carolyn, the most interesting investigator in the game? This will not stand.
The Combat Medic
Carolyn Fern is an especially durable Guardian with a powerful ability and effect. Additionally, her deckbuilding options are extremely broad, enabling great flexibility in her builds. This is both a blessing and a curse (appropriately), as one can feel inundated with decisions and suffer from option paralysis. Additionally, the devs seem to value flexibility very highly when creating characters, resulting in Carolyn having a base stat total of only 11. Her increased durability (she has an extra point in health/sanity) offsets this, but I would say a stat point is more valuable than health/sanity, so it's a bit meh.
What Makes Her Great
Carolyn's deckbuilding options combined with her ability open up a massive array of options that totally warp how a player should value cards. What do I mean by this exactly? Take First Aid, a fairly lackluster card that few Guardians can find room for. In Carolyn's hands, it can not only bring an ally from the brink of insanity but also allow them to afford their expensive assets. Clarity of Mind becomes a similar tool for both saving and paying allies, despite being maybe the worst horror heal in the game overall. Once higher level cards become available the the player, one's options expand into truly ridiculous healing tools like First Aid(3) and Ancient Stone(Minds in Harmony). On the other hand, those two items are basically the only high-level horror heals that your allies will care about.
A sidebar on Ancient Stone: With Shrewd Analysis, one can upgrade two copies into Ancient Stone (Minds in Harmony) for only 3xp. This is well worth one / slot, especially since the stones free up their slots after being upgraded. Identifying it can be tricky without devotion to clue-gathering, but shooting for a total of 4+ is very strong, since it neatly counters Rational Thought.
Basically, Carolyn fundamentally alters the value of many sub-par cards, increasing the amount of viable includes while deckbuilding.
Carolyn has so many options that it can be helpful to focus on a strategy and include some core elements, filling out the rest of the deck as one sees fit. To that end, here are some effective cores:
Dr. Milan Christopher
St. Hubert's Key
This is a build with very strong static increases to investigation. With everything in play (which ostensibly includes Charisma, a superstar include for Carolyn) the investigator is up to 8 while investigating. This would require a massive amount of resources, but I have done it. It also makes identifying the stones fairly easy.
Clarity of Mind
With these assets Carolyn is able to bankroll her allies, feeding money to the fighter so they can afford their expensive weapons. With xp, Stand Together is an incredible value both xp and card-wise. Inspiring presence can also be used to heal and recharge your own or your allies' Beat Cops.
"I've got a plan!"
This build uses guaranteed damage to deal with enemies and Carolyn's tankiness and healing to soak shots. Between her ability, Stick to the Plan and Emergency Cache, she has consistent access to guaranteed burst damage, despite it being fairly resource/xp intensive. In any case, "I've got a plan!" is and has always been a very strong outlet for damage, despite its one-shot nature, and I feel Shriveling would need a lot of support (from St. Hubert's Key/Holy Rosary, Arcane Studies, and/or Peter Sylvestre(2)) to be effective late-campaign.
Other Strong Cards for Carolyn
The big man on campus can provide you with a constant stream of resources, while providing his static stat boosts and infinite horror soak as usual. Combined with a reliable way to take horror, Peter becomes an enormous economy card rivaling Dr. Milan Christopher. Speaking of which...
With Carolyn's ability to heal horror, this is very safe to take. If Peter Sylvestre is in play, you double your resource gain and take no horror, which is quite strong. Cautious players (or those on higher difficulties) might opt for Painkillers instead, since it can provide fast, reliable horror in much the same way while shoring up Carolyn's low health.
In every Carolyn deck I've ever built, I've ended up with more than four ally cards. Especially if you decide to go with Foolishness, one or even two copies of Charisma will enable Carolyn to maintain powerful effects on the board, such as Dr. Milan Christopher and Peter Sylvestre, or Alyssa Graham and Dr. Henry Armitage, or Foolishness and Peter Sylvestre. Her allies are incredibly useful.
Similar to Charisma, Ever Vigilant allows Carolyn to setup for the whole game in a single action. I prefer assets over events for horror heal, so every deck I build with Carolyn has more than 20 assets. In this case, Ever Vigilant is incredibly strong and will likely be useful even late in the game, especially if you've found yourself without actions to play cards and great assets building up in your hand. This can also go under Stick to the Plan, although Carolyn doesn't have quite as many viable options for that card, so it might be overkill. I think taking aggressive mulligans for Ever Vigilant is probably the better strat, as it saves you 6xp.
The most effective strategy is probably to combine two of these cores into a deck that can take useful actions at any point in the game, for example by combining the Cluever with the Support suite. Or one can be more adventurous and combine everything they think is cool into some kind of monster. The options are quite vast.
Signature Cards and Weaknesses
Hypnotic Therapy is a very good card. Being able to heal one horror from any investigator every turn for the rest of the game is ridiculous, and it draws that investigator a card, and you can give them a dollar with your ability. If this is the only horror heal you get in play, things start to stabilize instantly. If you get it into play later, it's a steroid for your other horror heals, so that's great too. I wish it didn't exhaust for both effects, but it would definitely be broken if that were the case. Rational Thought, her corresponding weakness, isn't nearly as bad as To Fight the Black Wind, especially with Hypnotic Therapy or Ancient Stone (Minds in Harmony) with four secrets on it in play. It is still very annoying, since you don't get the benefit of your ability while it's out, so it can hurt your income. In my experience, it hasn't affected me at all, but I have yet to draw it when we're all about to go insane and I'm low on healing options. In any case, Alyssa Graham is useful to avoid such occasions.
Foolishness, her replacement signature, is very good, but also very annoying. Aside from needing a bunch of support to come online (which, admittedly, pays you back a bit), he also takes the ally slot, which is so incredibly valuable. I think he becomes more attractive in a four-person party where other investigators need Dr. Milan Christopher or Peter Sylvestre more than you do. To Fight the Black Wind, the corresponding weakness, is extremely terrible and can result in the agenda flipping a turn early if drawn in the upkeep phase. Ancient Stone (Minds in Harmony) is also very good against it, as long as you draw it with some actions to spare. There's certainly an argument to be made for taking all of her signature cards, since they do have some synergy with each other, but it is resource intensive.
Carolyn is one of my favorite investigators, probably for the same reasons that many seem uninterested in her: she's super weird. Her versatility is incredible, her ability is interesting and strong, and has no phase/turn limit, and her stats are strong enough that she's a competent investigator before applying any bonuses. Still, she has her downfalls: I've frequently found myself in scenarios with no horror to heal, which makes me value Forbidden Knowledge a little more highly. Her effectiveness is also highly campaign-dependent, I feel; she has plenty of horror to heal in NotZ and Carcosa, but less to do in Dunwich. In Forgotten Age, I think she's downright bad because the campaign throws far more damage at one than horror and her is garbage. With its focus on "the ethereal," I'm going to assume the Circle is also heavy on horror, so she might function quite well there (investigators are generally pretty powerful in their release campaigns).
Anyway, I hope you've enjoyed this review of Carolyn Fern. Thanks for reading.
Carolyn can't take Monster Slayer; I'm an idiot. Good catch @Death by Chocolate.
Added Dynamite Blast in the Combat build; she's one of the few s who can afford it, and I forget how good it is; good call @Swekyde.