Rick, I'm gonna come at this a bit sideways. Clays shooting is wonderful fun and can get to be an obsession with some folks. Some shoot simply to improve their field shooting, some to compete, some simply because it's fun.
But every one of them wants to break targets.
Within practical limits, as with most things, it's the Indian, not the arrow, and a LOT of clays shooters buy and sell shotguns looking for "the one", like golfers looking for the latest greatest driver. Now that's kind of a fun thing in and of itself, but it doesn't break targets.
The advice I give anyone wanting to get into clays is to look at something like a Beretta auto. These guns are soft shooting, reliable, and have adjustable stocks--very important, critical in fact. Without a proper stock fit you'll shoot nowhere near your potential.
You can find gently used Beretta 391s for less than a grand. With a little tweaking you can make it into a quite serviceable target gun.
And here's the most important thing--use the rest of that 2k budget to get lessons and buy bullets. Lessons from someone who knows what they are doing will do more to break targets than ANY gun you buy. With lessons and a 391 you'll break far more targets that you will without lessons and a Perazzi, guaranteed.
The first thing a good instructor will do is work on your mount and help you determine fit, which is something you can adjust on the Beretta much more easily and less expensively than you can with an O/U.
After that you'll have an understanding of what you're looking for in regard to fit and handling, and if you really get into the sport you'll save a lot of time, frustration and money on your journey to the perfect gun for you. And as you get into the sport and shooting a lot you'll be exposed to a lot of guns. Most people are pretty good about letting you handle and shoot their guns.
You could find the gun for you might just be the auto--many national and world championships have been won with the 391. Or it might be an O/U, but going into the search with a basis of understanding of the kind of fit and handling dynamics you're looking for will save a lot of frustration, and the best way to get that understanding is working with someone who knows their stuff and exposure to a lot of different guns. And the most efficient way to that point is a good auto, tweaked to fit you, and a LOT of bullets thrown at targets.
It shouldn't be hard to find a very well qualified instructor in your area.
