Question: I am currently working on an application in WPF/C# for personal use. I am not a "classically trained" programmer. Simply a hobbyist that likes to code in his spare time. Is there any accepted approach to the progression of application development? I. E.; Make it work, add fault tolerance, create a gui, then performance optimization. Or maybe should I design the entire GUI first? Basically I am going to start a new project soon and would like to have some sort of "every program needs this" checklist.

Answer: 
I'd say first of all, as simple as it sounds, write (either on paper or in your head) what the app is actually going to do. (Most businesses can't even do this part!)

Knowing that, sketch on paper what you think the screens will look like.
For example, say you're writing a home budget program and you want a drop down for accounts, and a grid for transactions, etc. Knowing what the GUI looks like will help tremendously.

Then fill in the details.
I try and take a look at my audience for the application. Then I'll create some use cases where I try and figure out what and why my application should even be built. Sometimes evaluating what you're writing and why you stumble across a lot of ideas that might shape the way you architect the application.

From there you can do as others suggest and put more importance on areas of focus.