Which synchroniser would you choose, and how do you decide?

The question behind the question is whether you reach for a primitive or for a queue, so answer with the decision rather than the list:

• One-shot event, "wait until X has happened": CountDownLatch, or a CompletableFuture if a value or a failure needs to travel with it.
• Repeated meeting of a fixed set of workers: CyclicBarrier, with a barrier action for the between-rounds work.
• The same, with a changing set of workers: Phaser.
• At most N at a time: Semaphore, sized after the resource, not after the threads.
• Handing data over: a BlockingQueue, or an Exchanger for a symmetric two-party swap.
• Fan-out and fan-in with results, failures and cancellation: CompletableFuture or StructuredTaskScope, not a latch plus a concurrent collection.

And the meta-answer that earns the point: if you can express it as a queue between threads, do that instead. A queue carries the data, provides the happens-before edge and gives you backpressure, which none of these primitives do on their own.