I believe it's what works for you, and when and where your ideas come to you. 

I'm not a game writer. I am developing film scripts for short films with the intention of directing them. In the process, I write the following: Vignettes, snippets, ideas, observations (truisms about life), dialog, outlines, and lots of lists. These often land in a notebook by pen if that's convenient when I conceive of them. I also send myself lots of emails, with the above.

For actual script writing, I use Fountain. It's easy and natural. Numerous apps and plugins support it. I use the Sublime Text editor with a Fountain plugin. The purpose of Fountain is to provide a clean, non proprietary, ASCII text file format for screenplay writing. Converters can convert it to industry standard Final Draft and PDF format. You can also include any kind of notes of your own format and making in comments in the file, If you're a programmer, you can write scripts that will extract this info and create numerous supplemental files to go with you project, including such things as prop lists, set descriptions, character descriptions, scheduling, etc.

The important thing is that when something really great pops into your head, that you write it down somewhere... anywhere... to put into your primary documentation later.  Having worked on the same universe for over 20 years now, it has become a part of my life to drop whatever I am doing, wherever I am, to write any good ideas down that come too me.  No matter where I am, and what I am doing.  I learned that lesson the hard way many, many years ago after having thought of things during the day that I thought were really important and then not being able to remember them later that night when I got home.

I call this "percolating".  A primary document has to exist so that it can "percolate" over time.  Little by little, it builds up into something great over time by all the little details that get added in this way.  The more of it that exists, the more there is to inspire such ideas to begin with.  So you want always want to keep the main document as complete as possible.  Until you write it down, you are still thinking about it.  Once it's written down you can move on to thinking about other aspects of it, and the depth of it all just keeps "percolating" over time.  Eventually you get to the point that you are working out the types of minor little details that other stories just don't have because they were written "all at once" and that person didn't have time to contemplate the minor details, or realize relationships between existing elements of the story that weren't immediately obvious when you first wrote it.

Most people probably don't have 20 years to let their story "percolate", but even over a period of 6 months to a year this would still wind up adding a lot, or changing a lot for the better that otherwise would never have changed.  And this process never ends until it is published.

13 hours ago, Kavik Kang said:

I call this "percolating".  A primary document has to exist so that it can "percolate" over time.  Little by little, it builds up into something great over time by all the little details that get added in this way.  The more of it that exists, the more there is to inspire such ideas to begin with.  So you want always want to keep the main document as complete as possible.  Until you write it down, you are still thinking about it.  Once it's written down you can move on to thinking about other aspects of it, and the depth of it all just keeps "percolating" over time.  Eventually you get to the point that you are working out the types of minor little details that other stories just don't have because they were written "all at once" and that person didn't have time to contemplate the minor details, or realize relationships between existing elements of the story that weren't immediately obvious when you first wrote it.

Kavik has nailed a salient point right here. I've always called it the stewpot. Let it simmer for a period. If it's not good, nothing will come out of it. But only after a few weeks at the minimum, and sometimes months, you'll see something else that will make it great. 

I do both. Personally I want to experiment with ideas on paper. For the game story I'm slowly developing I have Google Docs files open (one or two) and one notebook. Plus a few 3x5 note cards for plot structuring ideas. I've written a few short scenes partly or fully on paper, but due to using them for a writing course this term I had to type them up. 

I have a journal I started earlier this year for thoughts and ideas outside that. Figured it would help me out, freeing stress and jotting something down ever few days. Doesn't actually do that job; I enjoy contemplating ideas instead of writing some down. I keep them churning in my imagination until I want to write them down. Talking aloud helps me tremendously too. 

A few stories are entirely done on a computer and some are entirely done, at first, on paper.