Do you have a shotgun of any type or can borrow? I'm a fan of "run what ya brung" for someone who is interested in getting started in clay target shooting and then looking around to see what others are shooting, perhaps trying a few and then deciding what works for you.
Are you fixed on an o/u? In a new gun an o/u under $1,000 doesn't get you that much compared to a semi-auto. Between $1,000-$2,000 you are getting into a modestly better range of o/u but are now in the much better category of semi-automatics.
But here are my choices. If forced to buy an o/u under $1,000 I'd buy a Baikal but I'd have to be forced. Under $2,000 a field grade Beretta or Citori and I expect I'd be just under the limit. I might also give a look at the Winchester 101. Over $2,000 one of the target grade Berettas (687 Sporting, 682E, 686E) or Citoris (525, 625.) Way over $2,000 a Blaser. WAY over $2,000 a Perazzi.
What you want is a gun that fits you, feels good in your hands, is durable, holds resale value, has interchangeable chokes and a barrel length of at least 30 inches. Clay target games favour longer barrels. Try as many types as you can and buy the one that feels best to you.