I am wondering is there a possibility that every time I logged in to my Ubuntu, the desktop is set to Gnome Classic (no effect)? It is too redundant to set and choose it in the login every time.
The login screen always uses a user's last successfully logged-in session type as the default. If you don't change it, it logs in to the same interface you used before.
If the problem is that GNOME Classic is not installed, install the gnome-session-fallback package. In particular, if the problem is that you are selecting Ubuntu 2D as the session type and you get something that looks like Unity, that's normal--Unity and Unity 2D (provided by the Ubuntu and Ubuntu 2D session types, respectively) look very similar and both have launchers instead of a bottom panel containing a window list.
Whether or not this is due to a bug, it is also possible to set the default session type manually, as explained here. (However, if you're experiencing a bug, that also might or might not work. It would be valuable information for the bug report though, for you to indicate whether or not it does, so I recommend trying the techniques there.)
If you are trying to run