Is it possible to move from an old mac to a new mac only selected applications and documents?
You can of course select and copy any documents you want: though you will have to select them manually. 

For the applications, it will largely depend on where they came from. Apps from the Mac App Store are linked to your Apple ID, and can be re-downloaded from the App Store onto the new Mac. 

Third-party software may work just by copying the application: though some apps may need an installer that adds additional support files. Apps may need serial numbers or other protection re-applied.

whether they are App Store downloads, or other software that requires an installer. Some apps can be copied