That's A Tough Order To Fill. You Need To Either Add A Little Cash Or Reserve Some Of The $4000 For Tweaking The New Used Car.
If everybody could go buy a nice car for $3000 to $4000 then almost everybody would be doing it.
I did get a very nice Chevy Impala, 6 model years old, two years ago, for $4000. It needed $300 worth of tweaking, a serpentine belt (just to know it was good), trunk support struts, and an intermediate steering shaft. The tires were good and the car was well maintained.
That's what you should be looking for. Look for a well maintained car, possibly with service records. Be open minded as to the brand and model and more concerned with the condition. Most people on this site recommend having the car checked out by a mechanic prior to purchase.
Here's what I'd do since you say you've "been out of the loop" on cars. I would look at quite a few cars in your price range before even considering a purchase. Really look them over and take a test drive. You will soon get a feel for what's a good deal and what's a bad one, hopefully.
The best car is the one in the best condition. Buy that one.