What metrics do growth product teams look at to define success? Which do you find to be the most important?

Growth product teams are primarily responsible for incremental revenue in consumer applications. They are also accountable for internal metrics that directly correlate to revenue. Examples would be engagement metrics on a page, conversion metrics, user acquisition, retention metrics etc. It's hard to define the most critical metric. A lot of that depends on what the growth team is responsible for. Incremental revenue is a good metric a growth team should own.

Personally, I've always used pirate metrics.

• Acquisition - Getting the user to sign up
• Activation - Getting the signed up user to realize the value of the product
• Revenue - Getting the user to pay for the product
• Retention - Getting the user to stick around
• Referral - Getting the user to refer someone else to sign up

These are solid high level metrics to measure the overall effect of a team. However, when running a specific experiment, these metrics aren't always the best to choose when measuring whether the experiment was effective. If you have a lot of traffic, then it's not such a problem. But most companies don't have the traffic to consistently measure Retention/Engagement. Which, then you'll want to pick a less precise metric, or rather, a more upstream metric (something that happens before the high level metric) as it will will likely have a higher conversion rate, which means you'll need less traffic required to conclude the experiment.

In regards to which I find to be the most important? It really just depends on where the company is at at the time and where the biggest drop is. Most people probably say Activation, but that's not really true for every company. 

Metrics depend on the context. The most important is to have metrics that are aligned and shared with other stakeholders (marketing, sales, engineers, etc.). That's the most critical part: alignment.

However, don't forget that metrics are just compass, and most of the time you don't have real influence over it. At Amazon they prefer focus on the input for example, as you can control it, than the output: if we display 10 articles on a webpage we can achieve this. What happens if we display 20? what is the optimal number of articles we should display?