We get a lot of repeat orders. I would like to be able to identify and segment first time, (new) customers so I can email a custom message to them. Or, have a way to show how many orders a customer has purchased when a new order comes. Like maybe a number next to their order (i.e. 5 if it is the 5th time this customer has ordered, or 1 for first time orders).

That is a helpful tool.
Mike ( dlss.ca ) has a repeat customer indicator that would help with that and it does show a number on your list of orders.

We took his idea and went a few steps further with it. We have four buttons there to match orders. The first one is email. The second one is name and the third one is IP address.
Yes, we do get orders that are related to each other that only match the IP. See image below.
The fourth button is an indicator that shows if the customer has a client account.
This first example image would be a customer who has no history and no client account.


Below is another image showing a customer with a very active history.
So we see this customer (actually a test account of ours) has 16 orders with the same email. 7 orders matching the name on the order and 10 orders with the same IP.
The red client indicator tells us the customer has a client account, but was not logged in when they placed the order. (It will be green if they were logged in)


Notice we have a message there telling us things like too many orders cancelled. We also get an alert if the customer has multiple active orders. This can help detect fraud or allow you to combine multiple shipments together to save on shipping.
Clicking any of the buttons performs a search to show you the matches. Clicking the client login (key) icon, takes you right into the client account so you can add notes (if there are notes on the client account, it will show on their future orders as well ) or make corrections to their addresses stored, or perhaps link their new order to their account if they were not logged in when placing the order.

It's a ton or powerful info/tools packed into a small (unobtrusive) space there on the order details.
Perhaps ect would consider a feature like this (or some of these) being native to the cart.
Or a plugin that can be purchased.
I expect not all stores will need these features.

Thank you very much. Just what I am looking for!