My recommendation would be a used Browning Citori over/under in 12 gauge, preferably with interchangeable chokes.
But if the budget is tight, you'll get a lower price on a used shotgun w/fixed chokes. You'd probably want Full/Modified chokes if you choose a fixed choke shotgun in order to get the lower price. As it happens, some shooters are always changing out their chokes. Others leave in the Full/Modified until they are stuck in the barrel and can't be changed. So they might as well have a fixed choke shotgun.
I say Browning Citori because you may want to sell/trade someday; Browning Citoris are popular; there's an active market for them when you want to sell/trade/upgrade. Of course, other shotguns are also used; it's just that more folks use Browning Citoris for shotgun sport shooting than any other shotgun. I say used because you can save more bucks that way. May find a shotgun already set up for trap, skeet, sporting clays, whatever. Save on the buck$. May get some gunsmith modifications already completed, extra chokes, gun cases, accessories, whatever.
An adjustable comb and adjustable butt plate are very desirable, as well as some kind of recoil-absorbing system, such as Gracoil or SPS (Stock Positioning System). As time goes by, you may want to go out an shoot several boxes of heavier-load Handicap (greater than 16 yards) rounds. That's a lotta shoulder pounding.
If you buy a single-barreled shotgun (Browning BT99) and then someday soon want to shoot doubles, you won't be able to do it. So my recommendation is to go two barrels/over-under from the gitgo.
Some folks say that you should use a different shotgun each for trap/skeet/sporting clays. Other shoot the same shotgun for everything, which is what I do. And what's really fun is to see a guy with a $12,000 Perazzi, Kreighoff, Ljutic, or Merkel get outshot by a kid with a Remington 870 pump. Which happens often. Because..........the engraving does not make the shotgun shoot better.
If you are in the Omaha area, I'll be pleased to take you to the range and help get you started. If you wish, you can start with my shotgun, which is a very basic Browning Citori Trap over/under in 12 gauge w/adjustable comb and SPS.
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Additional Comment:
Wouldn't recommend a very low end shotgun (Stoeger, whatever). Bought a couple and shot them. Barrels wouldn't register (meaning: both barrels wouldn't shoot in same place on pattern board). Took them back to gun store, with great resistance from manager. Showed him the pattern papers. Still balked. Finally got store credit. You kinda get what you pay for, for the most part.
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Beware, it's a highly addictive sport.
Pull!!!!