Been shooting a lot of trap over the last 2+ years and own a couple of trap guns.

Personally, I would recommend either an O/U or a single barrel shotgun. Nothing against semi-auto's, but you will not be popular on the line if your gun is ejecting shells at your neighbor. There are fixes for this, but I think the O/U and single barrels are generally less finicky and less likely to cause you problems on the line.

As other posters have pointed out, you can spend a lot on a trap gun. It is definitely worthwhile considering a used shotgun (if it is a high quality one). A well made gun is capable of shooting 100,000+ rounds with only minor servicing, so you shouldn't be scared of a used gun.

If you have the budget, I would look at Browning and Beretta. The Browning BT-99 is a very popular single barrel option and you will see a lot of them. Browning Citori (which I have) is also an excellent option. As is a Beretta Silver Pigeon.

If you can, it is worthwhile shouldering, and even shooting, a few different models. Fit is critical to getting decent scores and the best shotgun in the world will not get you good scores if it doesn't fit you. I would therefore suggest an adjustable comb, which will help you get a good fit. Also, if you plan to shoot nothing but trap get a dedicated trap gun.

As others have said, most trap guys are pretty friendly and, if you ask nicely, will let you try their gun ... although I wouldn't walk up to a guy with a $15,000 Perazzi and expect him to let you shoot it.