Which Application Sub-Folders?
Your web server account will, of course, have to be able to read all of the files in your application folder.
The two sub-folders in your Logi application folder that will routinely need to have Write permissions granted to them are rdDataCache and rdDownload. The latter is often used as a convenient place to hold temporary files and does not necessarily have anything to with actual downloads.
If, in the course of your development work, you add your own new sub-folders to hold data files or "save files" used with elements like a Dashboard, or decide to write data to another folder, you will need to grant Write and possibly even Full Control permissions to them as well.
One approach that guarantees access is to give Full Control permissions to the Logi application folder itself (which is what Studio's New Application wizard does). All files and folders within the app folder then inherit the permissions. However, this is not necessary and, as mentioned earlier, may cause security concerns.