With a $3000 budget, the world is your oyster.

Again, my preference would be for an O/U or single barrel. And if it will be used exclusively for trap, get a trap gun. As others have explained, it will be designed to shoot a rising bird - i.e. if you were to put the front bead in the center of a bullseye 60, 70 or 80% of your pellets would be above where you were aiming.

If you're going new I would focus on Brownings and Berettas. If you're willing to buy used you might be able to step up to a Browning 725. You could also probably find a Perazzi TM-1 or a Ljutic Mono.

And I'm going to respectfully disagree with one poster about the risks of getting a "worn out" shotgun. My main shotgun is a Ljutic that I bought used a couple of years ago. The gun is 30 years old. I suspect the prior owner put tens of thousands of rounds through it. I've put 7-8000 rounds through it. I have had zero issues with it and suspect the gun shoots as well today as when it was new.

One of the guys I shoot with has a Beretta DT-10. He has probably put 100,000 rounds through that gun. Another guy shoots a Perazzi. Again, he shoots about 15,000 rounds a year and has owned the gun for approx. 10 years. Other than a couple of minor parts he has replaced himself the gun has been 100%.

That's part of what you're paying for when you spend $2-3000 on a shotgun, particularly a single barrel or an O/U - quality and reliability. And if you want to go used take a look at Joel Etchen, and Indiana Gun Club (a guy named Michael Gooch). Both will have a very good selection of high quality used guns.