Well… I made lists for the Villages and the Smithies, and I still like making lists. So here's one for this category. Sort of. The category "single-card engine" is nebulous and misleading, as the preceding argument proves all too well. The fact is, virtually no card in Dominion perhaps save Minion is good enough to be an engine entirely by itself (not even Scrying Pool)- even HP and Lab need Treasure to work, and besides "single-card engine" encompasses a wider variety of mechanisms than are really coherent. In particular, Minion and Nobles work really differently than most of these cards.
So I'm going to try and redirect this conversation to where it should have been at the beginning: Compare the Labs. By Labs I mean what the OP was roughly going for: any card that provides +1 Action and *at least* +1 Card with a chance for more, Laboratory being the most basic iteration of this idea. In other words, non-terminals which have as their function increasing your handsize. That's a much more coherent category. It also means some additions and subtractions to the OP's list: welcome, Apothecary and Caravan. Goodbye, Minion and Nobles. (You're great cards but you don't really fit here). Sorry Scout and Shanty Town, you can fizzle; sorry Warehouse and Cellar, cycling is nice but you decrease handsize instead. I'll let Activated Cities stay in, though the +2 Actions isn't shared by any other cards here.
I'm not going to bother putting them in tiers. But there are a couple natural gaps: the best Lab is noticeably better than the rest, and the worst is similarly worse than the rest. Most of these cards are quite good.
1. Hunting Party I'm not going to rehash in detail all the reasons why Hunting Party is REAL ULTIMATE POWER but suffice to say, it is. Ninety percent of the time, it's a strictly better Lab: probably a little worse as a 5/2 open and if you buy too many the last one'll just Chancellor you, but it's a better enabler for Big Money and it's better for sifting through junk and it's a better enabler to play your one linchpin attack over and over and it's a better enabler for Conspirators and many other chains and… you get the idea. Imagine if Village was a top-tier card already, and then Farming Village came along and it also cost $3. It has a better "win rate with" than any card that isn't a Prize, a curse attack, or Platinum; and its win rate without is nearly as impressive. We're talking about the best $5 non-attack (better than Wharf and Tactician IMO), and probably the third-best $5 overall. Hunting Party is cool, and by cool I mean totally sweet.
2. Menagerie Bet you didn't expect Menagerie to be this high! Well, it is. Unlike HP, Menagerie requires support to work well, but that support consists of "any trashing, at all, or maybe just the presence of hand-reduction attacks, or heck, cycling, or disappearing Actions like Festival/FV…" In other words, it's very rare to find a board that doesn't support Menagerie at least a little bit. And, well, when you can get Menagerie to work, it's *twice as good as a Lab* for *barely half the price* and is even better than that against Goons/Militia/Ghost Ship. Even if it only works a third of the time, that's not just a bargain, it's a bargain that makes Fishing Village look overpriced. Oh, yeah, Fishing Village, which goes great with Menagerie and is its primary competition for third-best $3 card. Obviously, it's kind of hard to get it to hit more than twice in a turn, unless maybe you're using it to supplement Minions or something, but it has so many other things going for it, and it's not like extra Menageries hurt. I buy it 95 percent of the time, and I don't think that's too much at all.
3. Laboratory The standard. Unlike Village and Smithy, the basic iteration is one of the best, and I say that as someone who is less a Lab fan than most people here. Most variations on Village and Smithy add bells and whistles, Lab is strong enough that most variations have to make it worse instead. Other cards on this list can sometimes give you more, or do it for less, but they don't have the versatility or dependability of good old Lab.
4. Scrying Pool In the right environment, Scrying Pool can be absolutely abusive above and beyond common sense, drawing dozens of cards at a time. And it attacks too! (Well, Spy is kind of a piddling attack, but still.) Problem is, the right environment is rarer than you think. If you can't trash your Coppers and Estates, or you can't get money (and preferably +Buy too) out of your Actions, then Scrying Pool is merely a Spy you had to buy a Potion to get. And that's no good!
Don't get me wrong, Scrying Pool is an incredibly powerful engine card, the situations where it is at least useful are pretty common, and I do like playing Scrying Pool unlike many here. But it is situational enough (and inconvenient enough to pick up) that it can't be any higher than fourth.
5. Caravan Pretty simple: a Lab next turn for $1 less. I think that the Duration effect is more damaging to Caravan than it is to, say, Fishing Village, because the +Card also has the effect of making it more likely to miss a reshuffle, and unlike FV it doesn't give any benefit this turn. It's a reasonably strong and reasonably cheap card, and it has the kinda-awesome property of making Workshop and Talisman actually worth it, but it's also probably not as strong as its reputation.
6. Activated Cities Talked about these a bit in the Villages thread, basically what I said there holds here too. One thing worth mentioning is that I think they really don't work without support, because without support a player just going for money and Provinces is probably going to be faster. Their potential is sort of like Scrying Pool in that way, but the triggers are much different: for example, Curse games are great for Cities, because they drain the pile, whereas they kill Pools dead. Cities also play much better with Treasure-based decks.
7. Apothecary Apothecary is only this low because all the other cards on this list are so good: I think it's actually quite useful and underrated. The most salient bit about Apothecary is that it improves both this hand and the next: you get Coppers to spend, and they're cleared out of your next hand. In the absence of good trashing, I'd even go so far to say it's better than Scrying Pool (Though of course its ceiling is much lower). Works great with Coppersmith and Wishing Well, and works even better than that with Ambassador: I've had great success recently opening Amb/Potion with the Potion just for grabbing Apothecaries. You cycle like a demon, pass back Estates, and have lots of Coppers to buy stuff with quickly. Requires a slightly different play-style, and is rendered useless by Chapel/Moneylender, but good Apothecary boards are way more frequent than you think.
8. Alchemist It's a Lab-plus! Except that it's really hard to get, and you have to really go out of your way to get the extra benefit, doing weird things like buying multiple Potions or Herbalist. It's great for building up mega-turns, if you've got Colonies and/or +Buy, but it's so slow and also fragile: hurt badly by Masq, Minion, and curse-givers. If it's just a Province game, chances are it's just not worth going Alchemist.
9. Wishing Well No surprise here. Its upside is merely a Lab, its downside is… far far more likely. Menagerie outclasses this card, in virtually ever way, so hard. I think it's a little better than people normally give it credit for, but it's still last here by a wide margin. If you can mass buy/gain them, Wishing for Wishing Wells is fun and sometimes profitable, and they work great with Apothecary (the WW/Scout combo is much worse and almost never worth it). And there's no harm and adding a few to your Goons deck. I think they're about as mediocre as Shanty Town, which I guess is fitting.