I need to move a Windows 7 PC to a different HW.
What version of Backupper can I use?
Is there anything to consider before performing backup fron the current HW and restore to the new HW, mainly if they are widely different?
Just backup and restore. Free backupper is fine. Maybe there is a Windows license problem. But besides that it should work. Mind that the new pc is a BIOS computer with a MBR disk. Not a modern UEFI machine unless you set that one to Legacy mode.
Are you keeping both PC's (asking per licensing problem)? If not, why don't you just take the old HD out and put it in the new build as your boot drive. If everything works and your license isn't a problem, then you can do a disk (or system) copy and restore to your newer HD or SSD. This way you will know if any problem you may encounter is related to AOMEI or to the upgrade.
I've updated multiple self built PC's by using the old system drive in the new computer without any problems. After booting, you can install the new chipset driver and then any other drivers needed for the new motherboard. I'm assuming the new build doesn't come with an operating system and this is why you want to copy it over. Is that correct? And that the new system has a better boot drive?? Just make sure the new system is using the same BIOS format (UEFI or legacy) for booting as the old system as JohnnyboyGo said. Let us know how things go. Good luck.