The reason to eliminate the car debt is simply to get rid of the monthly payment. At the end of the day though, either route I go (eliminating car debt or CC debt), I will still be paying out of pocket monthly to eliminate the remaining debt as is. That is why I asked about the 401k loan, as that would be a payment with minimal interest essentially to myself instead of to the CC company or to Toyota for the auto.
I'd stick with my original suggestion of getting rid of the credit cards first, then the car. I would not be in a hurry to pay of the student loans or the mortgage, depending on interest rates. But the fact that you want to get rid of the car is a factor. I might do what you say and bank the pending bonus until you sell the car and use it to make up the shortfall. I think it is a fair plan if you will not be buying another car until you can save enough cash for it.
Your idea for taking out a 401(k) loan seems sound on the surface. But I'd agree with the others here that taking one of those loans can be a really bad thing to do. There are lots of pitfalls. However, if you have extremely good job security and if you will be 100% committed to repayment then it is an option to consider. It's definitely not something I would do personally though.
You should do your budget in a way that makes sense to you. It's good to have (at least) the level of detail that Eagle suggested. I personally don't like the fixed/variable breakdown but if that works for you then it's fine. The F/V breakdown always makes me think of fixed and variable costs in a business. A person does not have costs that vary with level of production so it just doesn't make sense to me. I don't like discretionary/nondiscretionary either because those categories have no real meaning to me. I can usually eliminate a nondiscretionary cost if I choose by changing my behavior for example. So they are as discretionary as anything.
The bottom line is, pick a breakdown that makes sense to you and use it. To me it is less about calling it a budget than understanding where your money is going. If you have a good handle on that then you are off to the right start.