when the Geek Squad transfers the data from my 7 machine to the new 10 desktop, will they be able to transfer all of the turbo files, so when I do 2019, the info will carry forward, as before?
If you used TurboTax desktop software for those years, the TurboTax *.taxYYYY data files and any PDFs you made are by default in the \My documents\TurboTax folder on Windows 7 if you went with the default. I would make another copy of them and save them on an external drive or thumb drive before your transfer to Windows 10 to have as a backup--just in case anything goes wrong during your transition to the new computer. It's actually a good idea to be backing them up anyway.
The computer guy should be able to copy all your files from your My Documents folder on Windows 7 to your Documents folder on your Windows 10.
Is the computer guy going to use the Windows 10 that comes with and is already installed on the new computer? If so, and if you want the prior year TurboTax programs to be on the new computer, you'll have to actually install them on the new computer. You don't necessarily have to reinstall them now, but be sure you save the installation files (CD or download) in case you have to amend a return in future years. If you purchased from the TurboTax website, the download installation files will be in your account for at least 3 years. As long as you have the *.tax2018 data file in the Documents folder of your new Windows 10 computer, next year 2019 TurboTax should find it and transfer it into next year's 2019 return.