First, make a backup copy of
/etc/default/grub. If something goes wrong, you can easily revert to the known-good copy.
sudo cp /etc/default/grub /etc/default/grub.bak
Then edit the file using the text editor of your choice (e.g. gedit, etc.).
sudo -H gedit /etc/default/grub
Find the line that contains
GRUB_DEFAULT - this is what you'll want to edit to set the default. You must know the full name of the kernel you want - e.g.
Ubuntu, with Linux 3.13.0-53-generic - along with the full name of the "advanced menu" - e.g.
Advanced options for Ubuntu.
You then combine those two strings with
> and set
GRUB_DEFAULT to them as:
GRUB_DEFAULT="Advanced options for Ubuntu>Ubuntu, with Linux 3.13.0-53-generic" (including quotes).
Save it, then build the updated grub menu.
See also: GNU GRUB Manual 2.02 or more specifically section 15.1.0 on setting the default.
Note: There is a method utilizing numbers to access kernels and menus but this is not recommended as it is unreliable when kernel updates occur.