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.
What has worked for me in the past is the following (high level) sequence:

1. Understand and record the requirements (who, what and when) - use-cases, feature list, flowcharts, service level requirements - whatever works for you (I am partial to use-cases though).
2. Understand and record the design (how) - class diagrams, sequence diagrams, screen designs, API specifications - start high level and drill down (could start development before complete drill down)
3. Implement - start with API/stubs and unit tests, then fill in the code, update unit tests and execute unit tests as you go.
4. System test - test the components operating together and fix defects. Don't forget about performance testing (check that you have met your service level requirements from step 1).
5. Package, deploy and enjoy.