Welcome to the madness!
If you look carefully you can find a good quality used o/u at your price point. Buy a gun with a reputation for longevity, not an inexpensive import. To most people this will be a used Browning or Beretta, but there are others as well. Don't be afraid of a gun with fixed chokes. It'll serve you well on the skeet field and be a bit cheaper to buy.
I know you mentioned a double barrel, but frankly don't count out a decent gas auto loader. The plusses are reduced initial purchase price and reduced recoil while shooting. Use the price difference to buy a few flats of target ammo and put some lead down the pipe at targets. If you decide to move to an O/U later you can sell the auto loader for pretty much what you bought it for.
One more suggested purchase is the book called "Mastering Skeet" by King Heiple. I bought a copy at Wholesale Sports last week for 50% off the $19.99 price. One of the best books I've seen on shooting skeet. For the cost of a round of targets and shells it could save a new shooter years of trying to figure out how to properly shoot the game