I know this question has been asked before but those questions typically lack specific details and result in answers that say something like "It depends what you are trying to do..." so the main gist of this app is that it retrieves remote data (ex. text) and object (ex. images).
Since PHP and python are the two programming languages I feel comfortable with I felt python was more suited for desktop gui apps.  I'm creating a desktop music player and here are some of the technical specs I want to include:

A sign in construct that authenticates user credentials  (Like
spotify, skype, league of legends) against a remote database (This
will be in mysql.)  My thinking is to create a web api for the client to query via HTTP/HTTPS GET/POST
A client side SQLite database that stores the filename, filepath and
id3 tags of the song so upon launching, the application displays each song in a row with the song length, artist, album, genre (Like iTunes)
Retrieve remote images and display them within the application's frame (Like skype displays a person's profile picture.)
Must be cross-platform (At least in Windows and Mac), look native in different OS's but the native look and feel should be easily overridden with custom styles (Ex. rounded buttons with gradients.)
Compilation for Windows and Mac should be relatively straightforward

Of the popular python gui toolkits like PyQt, PyGTK, Tkinter, wxPython, Pyjamas, PyGObject and PySide which are well suited for my application and why?  Why are the others not well suited for these specs?    Which have good documentation and active communities?
Both PySide and WxPython support all five of your requirements. WxPython uses actual native widgets and also has custom extensions and widgets built on top. It has goodies like wx.CallAfter which'll allow you to run your background tasks in a separate thread and hop back on the UI thread easily. 
PySide has a nicer API but draws its own widgets that imitate the underlying OS's UI. It's not as mature as WxPython and packaging it with tools like cx_freeze and PyInstaller is slightly more involved.
Also I recommend that you use an ORM like peewee over plain Sqlite3 for the data storage, it makes managing the data a lot easier and plays well with the freezing tools.
Considerations for python gui toolkit for app that queries remote database?