The strongest individual cards to look out for in those sets include:
* Chapel (and Sentry when you have $5 on T1 or T2). Getting rid of your starting coppers and estates means you can draw your whole deck every turn which means you can do a lot of stuff. On boards without those but with other trashers (Moneylender, Remodel, Sailor, Salvager, Lookout), you still want to be trashing your starting cards, but it'll happen slower.
* Witch, Sea Witch. Curses really hurt. Blockade also conditionally curses, so it can hurt when you play blockade to gain the card your opponent really wanted
* Outpost. If you're drawing your deck every turn, Outpost means you're drawing your deck twice every turn.
* Monkey and Wharf. Those can both draw a whole lot of cards without spending a lot of +Actions per card drawn, and drawing cards at the start of your turn helps there. Smithy and Council Room do the same thing but slightly worse than Monkey and Wharf usually. Laboratory, Sea Chart, and Caravan can draw cards without spending any +Action, but those piles are liable to empty before you have enough of them to draw your deck.
* Fishing Village and Tactician. These both give you +Action at the start of your turn, which means if you're trying to draw your deck every turn, these mean you're less likely to draw a dud hand that lacks the extra +Action needed to kick your turn off. Note that Tactician is situational, and it's best when you don't need to play treasure cards (i.e. you've trashed them all and your payload is with action cards like Festival or Remodel)
* Throne room. Can often be thought of as reading "Choose the best card in your hand. Get +1 Action and play that card". +1 Action and do the Witch effect, for instance, is really good. It can even do village things if you play a throne room on another throne room.
* Smugglers. If your opponent gains a good $5-6 card, you can also gain a good $5-6 card.
The strongest synergies to look for in those sets include:
* Any kind of village (Village, Festival, Native Village, Fishing Village, etc.) + Any kind of draw card (Smithy, Wharf, etc.). This is the way you'll usually draw your deck.
* Remodel + (Bandit/Pirate). If you had the Remodel anyway (e.g. to trash your starting estates), then a gold gainer is a better way to get golds (which you'll then turn into province) than buying golds. You can also use Mine or Treasure Map on some boards, but often that's slow.
* Workshop+(Gardens/Island). Fast way to get a bunch of points. If you can't draw your deck, the optimal strategy will often be Workshop+Gardens+(some kind of village). If you can draw your deck, a $4 victory card can be a good reason to take an extra workshop, to put you in a position of being able to score extra each turn.
* Vassal + Some kind of village + Some kind of trasher or some way to look at the top of your deck. Vassal is really strong when you can make it hit an action card, but if it doesn't hit an action then it's awful. It's more likely to hit an action if you can trash your starting cards, and if you can make sure the top card is an action card (via Artisan, Sentry, Lookout, or sometimes Sea Chart or Harbinger), then you can make sure the Vassal hits one.
* (Haven/Island)+Gardens. Gardens wants you to have a lot of cards. Drawing your deck is harder when you have a lot of cards. Island can let you get the VP from a card without having to draw it. Haven can set aside a card before you shuffle, meaning you don't shuffle the set-aside card in, meaning you don't have to worry about drawing it instead of your other cards. Haven and Island are also useful for doing this with Provinces and Duchies, but it's often not worth the extra time to pick up the extra card with just Provinces.