I have 3 on-premise Exchange 2013 systems, I use 2 for active mailboxes and one for testing and backup if 1 of the others fails.

Ideally I'd like to install CU8 on the 3 system first, how long before I do systems 1 and 2.

Thoughts or ideas?

I had to update one of our 2013 MBX/CAS servers (non DAG member) to CU8 due to a journaling/archiving issue. Microsoft support wanted this server to be at the latest build to rule out issues/bugs from earlier CUs. The 5 servers in the DAG are still at CU4 and we are not actively planning to update them in the near future.

If your 3rd Exchange server is not a DAG member, then I'd say it's up to you.  If you have a DAG, once you decide to update them, they should all be at the same CU level.  CU8 does require schema updates, so I recommend backing up AD first.

yes, they are all 3 in the DAG, system 3 is 3rd failover choice.

Do I need to take them out of the DAG, upgrade and then add back to DAG?

I was hoping to do system 3 and sit on it a week or so to monitor it.

Bring up this article:

https://technet.microsoft.com/en-us/library/dd298065(v=exchg.150).aspx#Pm

And click on the link "Performing maintenance on DAG members"

And also read "Installing updates on DAG members"

It doesn't say in the article how quickly to upgrade them, but I wouldn't wait too long incase you have DB failures.  Are your DAG members in the same site or different sites?

I would put them in maintenance mode and upgrade 1 at a time but you don't have to do them all at one.

No you dont take them out the dag.

Here is a link to the scripts if you want:

https://gallery.technet.microsoft.com/Maintenance-Mode-for-6ded6984

You can do your test system and then a week later the rest.