I will be replacing my modem to a newer Motorola modem

It's generally automatic for all manufacturers. Because firmware has to come over the cable side, it's actually not possible for the customer to install a firmware update.
(Well, actually, that's not strictly true. But you'd first have to find the binary file for the update, then dismantle your modem and solder in a serial interface, and then unless the update is approved for use on our network the headend might roll it back during nightly maintenance anyway, so we can basically say it's not possible.  )

I see one of the "tags" on your post is "6141", so if that's the model you're getting I can tell you that it will be updated to firmware 1.0.6.12, probably within 24-48 hours of installing it.

We do take a while to deploy new versions once the manufacturer releases them, because we test the heck out of them first. But then they're automatically rolled out nationwide in small batches until all units are updated.

On some models we find that updates aren't strictly necessary, so several different versions are allowed to be active on the system, but we will update them on request to the latest version and Tier 2 and Field technicians will update them if they feel it will be helpful, but those are getting standardized lately as well. For example, I think every DPC3010 has the latest version now.

But to summarize my too-long reply: Don't worry about it. 

A moderator here might be able to take a look, but usually you just hook it up and it updates itself. Sometimes it might take a few days for the system to catch up, but generally it updates to what ever the ISP considers the best firmware for your area.

Thats the thing about firmware, a lot of time manufacturers will release updates that patch issues just with some ISP's or add features only certain networks can use. Other times, some firmware updates can cause problems, so they are usually tested for a while before they are considered OK. Thats why it takes a while after new firmware is released before it "might" be pushed to your modem. 

Kip, jinx you owe me a cola.