It's true, Windows 10 is compatible only with QB 2015 and later, you should opt for 2017 and get the extra 2 years of support.
It is best to "step up" the conversion, e.g., from 2009 to 2012 to 2015 to 2017, to avoid problems with your file. If you cannot do that, you can try the conversion yourself and if you have problems ask Intuit for help; they should do it for no extra fee.
Install 2017 on the new computer. On the old one, run Verify, then Rebuild, the Backup. Save the backup to a flash drive. On the new computer, copy from the flash drive to your hard drive. In 2017, click File > Open or Restore > Restore backup.