[data transfer] Old PC to New PC

Hi Everyone, I'm upgrading my parents computer from a core 2 duo to a i5 6500...

Heres the question, the old OS is 32 bit, the new of course is 64.

Its a good chunk of data. I've got a 3TB WD Mybook to transfer to, but whats the easiest way to do this. I assume if I just use the "backup" tools included its not really the best way to transfer data.

I'll do it one file at a time if I have to but was hoping there was a nice easy way.

Any thoughts? Guidance? Good jokes?

Thank you for the support and assistance