Is it better to copy/move my HDD to the new machine and then do an upgrade
Not possible for two reasons.
- The current Macbook Pros use PCIe flash storage, the drive from your 2008 model will not fit.
- The operating system in your 2008 will not run on a new Macbook. So you are going to get stuck at a kernel panic page.
What you should do:
Start the old computer and connect to the local network. Do the same with the new one.
When the new computer asks if you want to run migration assistant, say yes. Follow the prompts to access your old computer and then leave it alone for a while - it can take many hours to process things.
Migration Assistant will copy your user info, documents, data, and work out which applications are compatible with the new system. End result, a new computer as much like the old one as possible. You will need to update most of your old applications, 8 years is several major versions of nearly anything.
It's much faster if you put the old drive in an external case and connect it directly to the new computer. If you know how (and have the parts) do that.