I'm working on my first game, a story centric experience. I have ideas on mechanics, levels, visuals, and what not, but nothing I can firmly decide upon. How does one consider what they want? 

In my experience, story comes after the game mechanics. 

Usually a story could be attached to a broad variety of games.  Consider how a thematic story can be equally applied to first person shooters, a real time strategy, a platformer, even a board game.  I can easily recall many hallmark games of each genre that have an object or person taken, with the story itself applying equally well to Mario, to the Halo franchise, to Angry Birds, to many other games.

Build your game's core mechanic, the thing you want to build upon as the first thing. When you've got an amazing core mechanic, build your story around it as a framework.

If your game's mechanic is not fun, story cannot save you.

1 hour ago, frob said:

In my experience, story comes after the game mechanics. 

Usually a story could be attached to a broad variety of games.  Consider how a thematic story can be equally applied to first person shooters, a real time strategy, a platformer, even a board game.  I can easily recall many hallmark games of each genre that have an object or person taken, with the story itself applying equally well to Mario, to the Halo franchise, to Angry Birds, to many other games.

Build your game's core mechanic, the thing you want to build upon as the first thing. When you've got an amazing core mechanic, build your story around it as a framework.

If your game's mechanic is not fun, story cannot save you.

My ideas is for a third person action/shooter with some fantastical elements added later on. I'd really like to make a non shooter game, but this idea is burning in my head haha. Shooter, non shooter, platformer or other style alike, I want to write games that have those features. 

I've considered this game to be an FPS in a way too, but not like your normal FPS of today. 

Experience.

The games you love were not the first things that their authors did. In addition, commercial games are team efforts, you might be surprised at how big those teams are - check the credits!

Uou need to decide which skills you want to invest in. Art, game design, music, programming, etc, these are all areas that one can dedicate a lifetime to mastering. Few people will be able to do all the above for even a modest game (exception that proves the rule: Cave Story?).

Start small. Make clones of other games, or mods. Hone your chosen skills. Try to find others who have the skills you don't - for example an artist friend can sketch concept art that could guide your visuals.

Keep your best ideas simmering, evolving, motivating you to improve. You'll be disappointed if you try too soon - imagine someone expecting their first painting to be the Mona Lisa!

When you have more experience, you'll have a better idea of what you want (based on your skills), what others will bring to the table, and the uncertainty of discovering the answer to the questions that are best deferred to leave the design space open for exploration.

For me it was about testing an idea on a small scale to see if an idea was feasible, looking for things such as, did the mechanic really play well in action compared to what I was thinking. I would still have the plot in mind and would do my best around building a prototype that would fit my vision but a tiny scale so I could sit back and say if this were expanded would this game still be plausible and would fit the game play and design aesthetics. I went through a lot of revisions before I nailed the idea I was looking for, maybe try prototyping and tweaking it a bit and play around with your builds. It takes time but I think it's worth the effort.