Updating my PC

If you are using CC and not older Creative Suite programs, you should not expect any problems, as CC allows a pretty nice license management, even if the computer licensed is not available (stolen, brocken, discarded, scrapped, ...). No need even to deactivate ( @John Waller : I never deactivate beforehand). 

I addition you can activate CC on 2 computers concurrently. So I would recommend installing, activating, testing and then deactivating and uninstalling on the old one, if that is what you want to do. 

See here for more info: https://helpx.adobe.com/download-install/using/install-apps-number-of-computers.html

Just for your information: I'm using currently 3 computers and I have 2 of them activated concurrently. Works great!

And just for people with older CS software: Be careful, as it will not be as straightforward with older software. You better have to open a new thread and ask a question for your specific case.

Always Deactivate (Sign Out) first. Help > Sign Out

https://helpx.adobe.com/download-install/kb/activate-deactivate-products.html

Signing out in any single app (e.g. Photoshop) will deactivate all apps linked to your plan.

No need to uninstall the software on your old PC unless you really want to. Deactivating is all you need to do to free up an activation for use on another device.