There’s two main ways to make your hand better in Dominion: either have good cards, or have a lot of cards. +Actions/+Cards subscribes to the latter philosophy; it’s one of the fundamental strategies in Dominion.
In descending order of importance, a good +Actions/+Cards engine depends on the following ingredients in the set:
“Good” is usually defined as 3 cards or better. Wharf is the primary exception: its +2 Cards on this turn and the next is simply too strong to ignore. In addition, Ghost Ship and Witch are attacks so strong that you’ll usually want to play them as much as possible; in that case, adding a Village or two can be a nice bonus. But you shouldn’t otherwise structure your primary strategy around a card that draws only +2 Cards; for instance, trying to build around Shanty Town/Moat just isn’t going to get you anywhere.
Only two cards do better than +3 Cards: Envoy and Council Room. Both are quite good; Envoy just requires that you build some redundancy into your engine, while Council Room’s primary drawback is alleviated somewhat if your opponent is playing a similar strategy (giving one extra card is not that big a deal if they’re drawing their whole deck anyway).
Of the four +3 Cards, Nobles is usually the most popular because it doubles as both +Actions and +Cards (and gives 2 VPs to boot!). On the other hand, Rabble and Torturer are much more powerful; Torturer in particular leads to extremely swingy games, since whoever gets their chain going first tends to dominate thereafter. And as CouncilRoom graphs demonstrate, Rabble’s attack isn’t that great early on, but when chained it’s an incredibly mean late-game attack.
Library is a special case: since the point of most +Actions/+Cards is to chain them all together, it’s only good with disappearing +2 Actions, or some way of getting back down to a small handsize (e.g., Vault/Library). Otherwise, you’re limiting yourself to playing around one Library per turn, which can be good in a Big Money-esque strategy, but isn’t really much of an “engine”, so to speak.
Most of the +Actions cards are pretty interchangeable. You can split them into two categories: those that draw a card (City, Village, Bazaar, etc.), and those that don’t (Nobles, Festival, Native Village, University, Fishing Village). Obviously, all else being equal, you’d prefer to draw a card over not drawing any, but the cards that don’t draw provide some kind of benefit (VP, +Buy, cheaper, gaining a card up to $5, or just being obscene). The exception is Shanty Town, which is a pretty terrible source of +Actions for a +Actions/+Cards engine, since the whole point is to draw it with other Actions.
Though technically an ideal deck has about the same number of +Actions as +Cards, you typically want a bit more +Actions as a safeguard against drawing dead +Cards; it’s much better to draw a hand full of Festivals than a hand full of Smithies. Moreover, in an Action-filled deck, you really can’t get away with playing a “blind Smithy”, since you’d be mostly drawing dead Actions rather than Treasure. This is why Fishing Village is easily the best source of Actions for a +Actions/+Cards engine: though it doesn’t draw a card, its benefit lasts for two turns and basically guarantee that you won’t ever be lacking for Actions. (Just be careful not to lose all of them in the shuffle, because of its unusual cleanup rule shared with other Durations. For instance, if you needlessly trigger a reshuffle on the turn where your Durations are active, you lose the benefit of the FVillages for another deck cycle.)
+Actions that also give Coin are extremely helpful; one of the common pitfalls of building an Action-oriented engine is forgetting to buy Treasure as well, and ending up with a self-drawing deck that still can’t buy Provinces. At the same time, over-investing in Treasure actually hurts your deck, because it clogs up your engine and reduces the likelihood of drawing the critical Actions. (This is why Hoard is not a great choice for most +Actions/+Cards engines.) So cards like Bazaar are nice for meeting two needs at once.
If you’re desperate for Actions, Throne Room/King’s Court can serve as an emergency source: either by playing them on a non-terminal, or by stacking them on each other, and then on a +Cards.
The most often overlooked of the key ingredients, and the reasoning behind Council Room, Worker’s Village, Wharf, and Festival. Massive draw engines take a little while to set up; by the time they kick into high gear, you’ll often end up drawing so much money that a single Province is a waste. In addition, your engine cards are cheaper, and you’d rather stock up on them than buy a single large Treasure. For instance, while constructing your deck, you’ll often prefer a Village and a Smithy over a Gold at $7.
Unfortunately, cards like Woodcutter are a bit of a liability, since any non-engine terminal has a tendency to clog up your deck. This is where Worker’s Village, Council Room, Wharf, and Festival come in: they’re the only engine cards that simultaneously address the need for +Buy. In their absence, Markets (as non-terminal sources of +Buy) are a good substitute, though each Market purchase does represent a missed opportunity for another engine card.
Sometimes this isn’t necessary: see, e.g., games with Fishing Village/Council Room, where investing in trashing cards (like the Upgrade) only slows you down since you’re drawing your whole deck by Turn 8 anyway. (This is especially true if Warehouse/Cellar is in the game, as they’re only useful if you have dead cards.) But for all non-obscene +Actions/+Cards combos, an early Chapel greatly optimizes your engine by weeding out the useless cards. (Of course, you should be mindful not to over-trash; as noted above, it’s easy to focus so hard on Actions that you finally draw your whole deck only to realize that you don’t have enough money in your deck to do anything.)
Or really, just anything that can deal with dead cards. Vault/Secret Chamber are good options, and Coppersmith could be considered in this category as well. But the ideal card is Warehouse: when your deck depends so heavily on a few critical cards, it’s definitely worth having one fewer card in order to make sure you draw what you need. They’re invaluable early on if you have no trashing, and they’re the only things that can keep an engine deck running through the late game green saturation.
Throne Room/King’s Court
More optional than the other components, but it’s a natural fit. Since the power of your deck comes from Actions, it’s only sensible that Action-multipliers would thrive. Of course, it works best when your engine cards provide ancillary benefits: Throne Rooming a Smithy is not nearly as fun as Throne Rooming a Torturer. And as mentioned above, Throne Room and King’s Court can serve as emergency sources of +Actions.
+Actions/+Cards engines are affected much more severely by Cursing attacks than handsize reduction. This makes sense when considering the quality v. quantity dichotomy mentioned at the beginning; being Militia’d isn’t that big a deal when you only need a few key Actions in order to draw your whole deck, but clogging up your deck with Curses really gums up your engine and makes it nigh-impossible to chain your cards together.
Finally, +Actions/+Cards engines take a little while to really get going. They often fall behind faster strategies while you try to draw your engine cards together; in these situations, it’s important not to overreact, since you’re giving up the biggest advantage of your strategy if you panic and buy a premature Province. A good chain can often end up buying multiple Provinces at once to mount a comeback; just be careful not to fall too far behind, especially when against cards like Hoard or Vault that allow a Province-buying opponent to maintain reasonably strong buying power.