Is there an easy method of backing up the AD config, services and files, installing the new OS and then restoring AD, Services and files?
No. There isn't. For a start, you're not 'backing up & restoring' these things, you're migrating them to a new operating system that delivers these old services in new ways.
The "correct" way of transferring AD to a new server is to bring up the new server alongside the current one, promote the new server to be a domain controller (and add associated roles, e.g. DNS), transfer all Active Directory roles that are on the old server to the new one then demote the old server back to being just a member server. This is what you should do.
I'd also have more than one server acting as a domain controller, by the way, its really not a good idea to have just one domain controller.
As for transferring "files and services", this depends somewhat on what they are.
There's a big difference between copying one or two files and copying everyone's home directory share, for example, when it comes to transferring files.
Same for "services" - there's a big difference between setting up a "simple" service such as DHCP (or even a complex, but mostly self-contained service, such as SQL server) and migrating Exchange from one server to another (especially Exchange on a DC).
If you're honestly not sure where to start then you might be best off hiring a consultant to help.