If you had to choose one metric to watch for measuring new customer performance, I'd pick profit from new customers.
This is based on a core business metric (profit) but segmented for new customers only. It would include the costs to acquire the new customers (CAC) and any overhead costs too.
As long as it's positive, trending up, and a good enough return, you'll know your new customer process is working well.
If costs are difficult to separate and calculate for new customers, alternatively revenue from new customers could fill in. You'll want to keep track of your total expenses too and use that as a break-even target (e.g. $200,000/mo in expenses means revenue should be at least $200,000 each month).
Actual profit is better though if you can get to it easily.
A quick and automatic way to measure your customer behavior is with Repeat Customer Insights. It'll automatically import your Shopify data and run a number of analyses to highlight different customer behavior.
Eric Davis
Retain the best customers and leave the worst for your competitors to steal
If you're having problems with customers not coming back or defecting to competitors, Repeat Customer Insights might help uncover why that's happening.
Using its analyses you can figure out how to better target the good customers and let the bad ones go elsewhere.