My Saturn does still run, but it almost takes more oil than gas... 225,000 miles on it... And I've had it for almost 9 years. So I think an upgrade is justified.

That's fair, honestly.

Would this be a logical purchase?

Everyone who's replied to you so far, with the answer of "no" should be enough to let you know the answer. The number of threads on this sub alone asking for help getting out of a scenario you want to willingly get into should let you know the answer. OP, I seriously wonder if this is a troll post.

So any suggestions on what my budget should be for a car? What cars should I look at?

I'm glad you changed your mind.

You make $31k. If your total monthly expenses are $980 including student loans, I'm going to assume you're still living with your parents. You're going to have to move out eventually, and with that will come rent, utilities, etc. If you have $31k worth of BMW, there's no way you'll be able to afford that. Your parents do not want you living with them forever, trust me.

The best thing you can do is pay for a car with cash. Some quick and dirty math says you're getting around $1850/month after taxes, right? So you can save $870 per month towards a new-to-you car? You have $4k to use as a downpayment, but what if you saved for 6 months? You'd have nearly $10k.

In the $10k range, I'd recommend getting something ~5 years old with less than 60k miles. In that time, learn how to drive stick. Sometimes manual transmissions sit around for a while, waiting for a buyer. They're also cheaper and easier to maintain, and in some areas, operate as an anti-theft device, because no thieves know how to drive one.

I'd go with a Japanese small sedan if I were you. Toyota Corolla, Honda Civic, Nissan Sentra. I'm a little biased, so I'm also going to recommend Mazda 3 and Subaru Impreza.