The first thing to do is understand your metrics categories. I have found it useful to combine Lean Analytics phases ("empathy", "stickiness", "growth) with the Pirate Metrics framework (AARRR: Acquisition, Activation, Retention, Revenue, and Referral).
Combining them goes like this:
Empathy phase: Are you solving the right problem? Use Acquisition and Activation metrics.
Stickiness phase: Does your solution adequately solve the problem? Use Retention and Revenue metrics.
Growth phase: Is your solution good enough that customers share it without being prompted? Use Referral metrics.
Depending on what phase you are in, you'll be looking more closely at one set of metrics over another. Go in the order above--as in, there is no point optimizing share rates until your retention is pretty solid, etc.
Now, for each "feature" idea on the product backlog, make sure you have a clear definition of which metric you'll watch to see if that feature was successful. Focus on one at a time. Have the team iterate until you reach some stable state in the customer lifecycle, and then move to the next metric.
So, for example, make sure your landing page articulates the value proposition such that you can acquire leads or customers at a cost that makes sense.
Technically? You can use Google Analytics for pretty much all of this. But if you want to get fancy, Mix Panel and Heap Analytics are also good (paid) tools for managing metrics.
The key is to focus on one metric (or set of related metrics) at at time.
PS: I cover this in more detail here