Regarding the Logic app, you, open to the App Store app, login with the same Apple ID on your new Mac that you used to purchase Logic and click on the "Purchases" tab. There is a list with all the purchases you made with this Apple ID. Click the download for Logic and that's it.
Regarding the other files, you might want to copy the following files over
"userfolder"/Music/Audio Music Apps/ Most of the settings files should be in this folder unless you used an older Logic version, then some files might also be in you user Library.Aplication Support/ folder
"userfolder"/Music/Logic/ These should be all your Logic Projects unless you saved them to other location that his default location
"user folder"/Library/Preferences/com.apple.logic10.plist/ This is your Logic settings file
"user folder"/Library/Preferences/com.apple.logic.pro.cs/ This is the settings file if you made configurations in the Controller Assignment Window
"user folder"/Library/Audio/Apple Loops/ If you have saved custom Apple Loops
In addition you might have to re-install any plugins or other related apps/files that you use in Logic.
(Plus, copy all the other important files that I forgot to mention 😉)
Hope that helps
Edgar Rothermich
http://DingDingMusic.com/Manuals/
'I may receive some form of compensation, financial or otherwise, from my recommendation or link.'