Which method should I choose to install GNOME?

There is a better and simple way available to install gnome-desktop using tasksel. Tasksel is a debian tool to install multiple related packages as a coordinated task. You will get many such tasks like lamp-server etc which can be installed in just one click.

Here's how to do that for gnome-desktop:

sudo apt-get install tasksel
sudo apt-get update

(Updating cache is necessary because you may get an error like this if you don't: tasksel: aptitude failed (100)

Then

sudo tasksel

• Select the Task Ubuntu GNOME desktop using spacebar and click OK.

• Ubuntu GNOME desktop will get installed.

One more thing: you may get the error tasksel: aptitude failed (100) again(it is a bug in tasksel for a long time) so just restart the system.

• You will get the desktop environment selection menu on login panel:

  1. GNOME Default

  2. GNOME Classic

  3. Ubuntu

Select the one you want, Enjoy.

hope this helps :)

Even I had this problem. So here is the solution for it. First use this command to update your repository

sudo apt-get update

after this, upgrade your repository with this command

sudo apt-get upgrade

now try to install gnome using the following commands

sudo apt-get install gnome-shell  
sudo apt-get install ubuntu-gnome-desktop

For me your 2nd method works great with

sudo apt-get install gnome-shell

But I also made a reboot after the dist upgrade. Try it!

sudo add-apt-repository ppa:gnome3-team/gnome3-staging
sudo add-apt-repository ppa:gnome3-team/gnome3
sudo apt-get update
sudo apt-get dist-upgrade
sudo reboot
sudo apt-get install gnome-shell