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: 
If this is something you're doing as a hobby, you can choose any development methodology you want.

Typically, for commercial development, there's some form of prototype made first (for WPF, SketchFlow with Blend is fantastic for this). This is typically required since you most often need to "sell" the concept, either to a client, management, etc.

However, if you're doing this on your own, you have the freedom to do things any way you wish. One comment, however. I would, personally, not thing of "fault tolerance" as separate from "making it work", however, since "fault tolerance" comes with testing, and unit testing as you go is much more effective...
This is a huge topic that will probably garner a lot of opinions, so I'll chime in with this: Test-driven development. Try reading about it, and make the effort to incorporate it into your development strategy as soon as possible. TDD is the one thing I wish I had known when I started writing software years ago. It makes a world of difference in the quality of the stuff you put out.