You want your entire hard disk to have encryption. You want to install Ubuntu Linux with partitions. What do you do?
Follow these directions, but make sure the second partition (with GRUB) uses 80 MB. To do this, mentally find this command "sgdisk --new=2:0:+2M $DEV" here:
When you get to that command, use this command instead:
sgdisk --new=2:0:+80M $DEV
We think the directions above would not work on many systems unless you allocated more space to the GRUB disk. The rest of the directions may be fine.
The LUKS unlock step (in the help.ubuntu link above) seems unnecessary or it may seem tedious if you have a long passphrase. However we recommend you try that step as it applies to the encrypted partitions you created.