Dominion strategies

You'd think with over 3 million combinations of cards (picking 10 of 25 different cards) then there would be a nigh infinite number of strategies to a game like Dominion. I've found this not to be the case but it's a subtle distinction. Every game is going to bring about it's own challenges or quirks. And most games will find that there's a single strategy that, in the absence of other players, is the "best". However, this determination is never easy and it is also never "absent other players". Here's a general breakdown of my thought process as I approach each game of Dominion.

What am I going to buy the first two turns? You always know you're going to have a total of 7 treasure in the first two turns. In the vast majority of games (somewhere around 83%) you'll end up with a 3/4 split (either 3 in one and 4 in the other or vice versa). So generally you want to have a good sense of the 3 and 4 cost cards. In some games you'll be lucky enough to have a 5/2 split which gives you access to some of the more powerful 5 cost cards 2-4 rounds earlier then your opponents (which can be very important for things like the Witch). Generally powerful cards you want to take a hard look at: Workshop, Militia, Moneylender, Remodel, Village. Those cards are almost always good buys early on (depending on the strategy a board might present itself with). The list gets bigger if you start including expansion cards from Intrigue or Seaside.

What are the defining cards in the card pool? There are certain cards that I think of as "game changers" and other cards that are "helper" cards. That's not to say there isn't a certain critical mass of "helper" cards that could form it's own strategy, but generally it's the "game changers" that define what the winning strategies will be. The ones in the base set include: Gardens, Witch, Chapel, Moneylender, Throne Room. Again, Intrigue and Seaside greatly increase this number. Each of these cards has some other cards that are needed and many of them fight against each other for a winning strategy. For example, if the Witch (give everyone a curse card) is in a card pool with Chapel or Gardens is value goes down tremendously. On the other hand, against a Moneylender strategy, Curses can be incredibly disruptive against a deck trying to be lean (especially if it's staying lean without being able to trash cards at will).

Are there enough "helper" cards for the "game changers"? Each "game changer" has a group of helper cards associated with it. For gardens it's going to be +Buy cards and cards that let you gain cards for free (Bureaucrat, Workshop, Woodcutter, Thief and Festival being some of the better ones). In general, I'd say the following are important

Gardens: Already listed
Witch: You really want to see an absence of trashing cards (Chapel and Remodel specifically). Cards like Cellar and Most are also nice to avoid.
Chapel: You'll need some + action cards with Festival being the best one but Village, Laboratory and Market being sufficient replacements. Mine and Moneylender can also help as can Remodel. Alternatively, Council Room and/or Smithy can accomplish much the same goals. You'd also like to avoid Thief if you can help it as that's going to hit you disproportionally as well. You wont' be buying many actions with this deck as your goal will be to replace all the copper in your deck with silver (thinning out the remaining copper) and eventually gold. Ideally, you'd have 4 golds and a chapel and then buy provinces every turn. This is why Council Room is so good with this strategy as it lets you draw 4 (many of which will be gold) and then make another buy (a Duchy, Gold or Province being the most likely).
Moneylender: Some + Buy cards are nice because you'll eventually want to buy multiple buys. Festival is the best of the bunch here because it gives extra coins and the ability to use a card drawing action in the same turn (as well as using the actions from that use).
Throne Room: Any card that does well in multiples is going to work well here. Market, Thief, Council Room are all very, very good. Adventurer pretty much guarantees you a province if doubled. A Throne Roomed Witch will make your opponents groan and a Laboratory is going to fill your hand and give you two more actions to do stuff with.

What are my options for +Actions: One of the first things that players grasp is the power of extra actions. +1 Card / +1 Action cards replace themselves and can be considered "free" (in a deck thinned down to silver/gold a Spy is strictly better than another silver). Cards like Village and Festival can form powerful action chains. Many new players get trapped into this strategy without accumulating enough stuff to do anything. I've seen many games where someone chained together three Villages, a Festival and Throne Room / Smithy and then bought a silver. On the other hand, a board with all terminal actions (i.e. no +actions or no reliable +action cards) can really change your strategy. In such a game you'll probably just prioritize money and a few select action cards (3-6 typically).

What are my options for +Money: Cards that give +money, especially if they give +actions, can be thought of (generally) as souped up versions of their respective treasure. This is why Festival is so powerful, it's effectively a silver that gives an extra action and an extra buy for only 2 more then a silver would have been. Compare this to Market which effectively is a copper that gives a card and a buy for 5 more than a copper and you can see why people generally prefer Festival over Market. Games with a lot of good "virtual treasure" can have a profound affect on other cards (particularly Thief and Adventurer but others as well).

What are my options for getting "free" cards: Typically, the only way to get a card into your hand is to buy it. Some cards put "free" cards into your hand or your deck. Cards like Bureaucrat, Workshop and Feast can have big impacts on the game. In the early game, these cards can be like having an extra 3, 4 or 5 treasure in your hand.

What deck thinning options are there?: The primary deck thinners in the base set are Chapel and Remodel. Cellar serves a similar purpose but doesn't permanently remove the cards (and still costs you a card to do it) but at least you get a better turn when you use it. Moneylender is a very targeted card (removing only copper) but does it really well (giving you temporary money in exchange). Adventurer and, to a lesser degree, Library can also be considered way to "virtually" thin your deck while Spy gives you some modicum of control over your deck. These cards go up and down in value depending on the other cards available. Thinning copper isn't as nice with a Thief running around. Library loses a lot of value if there's a lot of curses in your deck.

Those are the basic things I look for at the start of a game. They're not all encompassing and occasionally I spot a crucial interaction after the first couple turns but generally it covers most things and gives you a basic place to start.