@Vincenzo -- there's another step you'll need to take if you're going to substitute a laptop for that old CPU. You'll need to change your settings so that nothing happens if you shut the lid on your laptop. Without that setting the thing will sleep or shutdown whenever you close the lid and that's not what you want. Instead you want to have the lid shut and switch entirely to the standalone monitor when you are using the computer in "desktop mode."
Once that is done, you have a great setup. You can use a standard keyboard, mouse and monitor at the office and still have a computer that has all of your work files and applications on it on the road. It's the best of both worlds, really.
For even more portability, use a free cloud storage service (Dropbox, Google Drive or Microsoft One Drive, for example) as the default storage location for those files you don't want to lose. You can access them from any computer or mobile device with an Internet connection and those files will be backed up, too.