It really depends on what you're planning to do with the computer. How versatile do you need it to be, are you planning to generate keys with that computer, for how much money, etc. Depending on that, what you need to do will change.

However, usually, no matter what, I would choose full-disk encryption (during the installation, not only the home folder).

Afterwards, I would make sure it's up to date.

On ubuntu and related distros :

sudo apt update

sudo apt upgrade

Then I would check to make sure I don't have open ports that I don't use. For example, if you won't be printing, you don't need "cups". You can look at which ports are open with :

sudo netstat -lntp

Those are some pretty basic but important steps.

For anything major in the bitcoin world, you can either choose to use in combination with a hardware wallet or go with a disposable computer that will never go online and use it only with a live-dvd linux distribution.