Having done both -- buying cars outright and financing one.. I definitely have to say: Buy them outright.
There is no guarantee nothing will go wrong with a car you just bought--in fact, a new car requires a bit of maintenance on top of that payment bill. If I were you, I'd save the money for the new car to the side and buy it in cash. They'll typically give you a better rate, and there's no dealing with interest and financing. While financing a car can help a person with bad credit, it does nothing good for someone with good credit standings already, and usually it is a pain.
I had an issue while I was deployed where my bank blocked a payment I made on my car.. and the bank, nor the bank financing my car, bothered to notice and tell me. I ended up getting it fixed, but it took nearly a year and completely destroyed my credit in the process because they kept insisting I did not pay them the final payment, and I kept sending them all the evidence that I had. It turned out to be a payment BEFORE the final one. They just sent me my title and everything anyways. They simply didn't notice that my bank had blocked it for a few days before allowing it to go through, so it said unpaid in their system. And since it was only one month before the last payment, and I paid twice in the last month, the clerks thought I paid it all off.
Oil changes, tire maintenance, and a lot of other things still go into new cars, and while I definitely won't buy a complete clunker of a car anymore in my life, I would definitely consider investing in a transition car that requires a little less maintenance than your current one, and save up your money for a new one. If something goes wrong one month, you aren't out any money--its just savings money. If something goes wrong with a new car, you're out the monthly payments AND whatever you need insurance wise/repair costs. It just isn't as stable.
Of course, spending $500/mth for repairs is definitely calling for a change either way.. I think you could probably owner finance a transitional car for that cost over a few months.