Someone talk me out of buying a new car please. via /r/personalfinance

Backstory: I was driving a 2010 Ford Fusion SE which was totaled when someone rear-ended me in their 94 Ford Pickup. It completely crunched the back, sent glass shards flying from the back window all the way into the front seat, and left just a tiny dent on the grill of his truck.

Fast forward to now: I owed $3k for the car and his insurance is paying me $8215 for the car, leaving me with $5k to go toward a replacement vehicle.

My current financial situation: I'm a non-traditional student going back to school for a degree in Computer Science and won't be finished until December 2017. I currently owe a lot of money on credit card debt accumulated to keep us afloat while I go back to school and can only work part time. I'm working an internship that pays $17/hour that allows me to work ~25 hours during school and 40 hours a week otherwise. My wife is currently unemployed while she takes care of our 3 month old son, so that makes finding a used car more difficult for me as well, since I can't get something too small.

Why I'm considering an old beater: With a cheaper car, I can start using the $300+ a month I'd be paying on a car payment normally toward paying off other debts, starting with what I owe on my phones still on the AT&T Next Plan and moving on toward the higher balance credit card bills. Insurance would also be cheaper since it'd be a cheap car hardly worth paying anything for if it's totaled so it'd be a double gain.

Why I'm considering a new car: There are several reasons I want a new car (specifically a Honda Civic) which I'll outline below:

• The monthly car payment will be roughly equal to what I was going to be paying on my old car for the next year anyway (Fusion was set to be paid off next August).
• I can get them to knock off quite a bit from the sticker price, so depreciation is less of a concern. The sticker price of the Honda EX-T with the add-ons they included at the dealership was $25k, and he's able to knock down to $20,660.
• Interest rates are incredibly low right now. Worst case scenario I'm willing to pay for a new car is 3.99% APR, which is higher than I'd like considering my Fusion was 1.74%, but still much better than the horror stories of 14%+ that Dave Ramsey wrote about in his 1993 edition of financial peace.
• Again on the depreciation thing, that argument doesn't work for multiple reasons for me, such as the car holding its value quite well after the price cuts, plus the fact that barring a car accident, I expect this car to last me 15 years (knock on wood) anyway. With an old beater, I'd most likely want to get rid of it not too long after finishing school and finding a decent developer job.
• Looking for a used car that's a good deal is incredibly time-consuming and stressful, especially on top of my current coarse load at school.

I'm really torn right now on which route I should take. I'd have peace of mind from both instances, either in the form of one less monthly payment to worry about, or not having to worry about getting a lemon used car that breaks down on me on my way to class/work/elsewhere.