You don't need art to get started. Just start programming with squares and circles.
TBH, my game has the art style it does because I can't draw ha! As Wreck said, start with simple shapes. My first project was a text-based, time-driven RPG combat simulator done in Code::Blocks.
As for a design doc. Limit it to scribbles and notes. Docs are a great way to limit progress, IMO. Note key elements, simplify the plot and get to experimentation. When you are confident in your skills at iteration then begin preproduction. Or even fly the whole thing blind, depending on your project. A friend of mine spent a good 3 months writing an entire doc for a game 2 years ago and sent it to Shuhei Yoshida, for some odd reason. Over 150 pages of gameplay elements, story, literally the entire game. Never heard back. He could have had a working prototype in that time and sent vertical slices to various development portals, started gaining interest for it online, etc. He still pretty much writes docs waiting for something to happen.
If you are just starting, experiment first to see your weaknesses and progress. Or quickly gather teammates to help you iterate. Seriously. Docs are mere guidelines. Many devs don't even use them. If you have your game in your head then what is stopping you from progressing? A doc won't get you iterating!
Grab Unity, Stencyl, Construct, UE4, etc. Start building small slices. Start building a team. No time like the present!
Thanks for the tips! (And sorry about the late reply )
I've actually been cleaning out my OneDrive account recently, due to all the leftover stuff from previous years that I don't need anymore, and I stumbled across the rules document I drafted in an attempt to make a board game that functioned kind of like a cross between Risk and Monopoly.
I'm gonna rework the rules a bit and see if I can't set it up in Unity. Hopefully it all goes smoothly, but I can't say for sure.