git init just on the Assets folder?

Would it make sense to initiate git just on the Assets folder, as the rest seems to be generated?

You don’t need any files inside the Library folder when you enable the meta files. (Editor Settings, check out the docs)

You only do need git to track those two folders:

  • Assets
  • ProjectSettings
  • (and the .gitignore file)

Everything else (Library, Temp, and project files) should be ignored (via .gitignore)

I have not worked out which files in the library to keep yet, but some are needed to associate your assets with the scene data. I deleted my library only to find that it ruined my scene. Therefore, i recommend initiating git for the entire project and using a .gitignore file to get rid of some of the junk.
Here is the contents of my .gitignore file based of what i picked up on a few sites:
(Note that I have not tested this yet.)

#Folders

/Library/FailedAssetImports.txt
/Library/cache/
/Library/previews/
/Library/ScriptAssemblies
/obj
/Temp

#File Extensions
/User Preference Files

*.sln

*.csproj

*.pidb

*.userprefs

*.user

*.suo

*.unityproj

#OS Junk

Thumbs.db
.DS_Store
*
ehthumbs.db
Icon7
.DS_Store