First, don't be ashamed of a 10 out of 25 on your first time out. I have taught many students to shoot trap and several have shoot 0 out of 25 and many less than 5. Maybe it is my instruction
I shot trap for several years with my 870 with a 28" barrel and fixed modified choke that I use for hunting. I shot singles, handicap and doubles. You also learn to run a pump gun through shooting doubles.
When I was averaging 21-23 consistently in singles, I decided to make the leap to a Trap gun. I went with a Browning over and under. My 870 is still my primary hunting gun.
My advice is get out there and shoot. Find someone who knows what they at talking about and have them give you help. Pay for good advice if necessary or you can afford it. Be careful, there is a lot of talkers out there that have marginal advice. Probably the two best pieces of advice I received were: "Wooden Stock, Wooden Head" and "Swing from your ankles". In other words, make sure to keep your head on the stock especially for bird cutting hard to your firing side. Secondly, when swing the shotgun, it is not an arm movement. Instead it is a full twist of the body. Finally, remember it is a very mental game. Keep focus and worry about executing the next shot perfectly . . . the one before and the one after don't matter.
Don't get hung up in the worrying about superior equipment, chokes, and add-ons to your gun until you can on the order of 80-90 out of 100. Get the fundamentals down. Especially in trap shooting, too many people think the equipment makes the shooter. Remember, Ping clubs don't make you a scratch golfer . . . but you do get high in style points.
As you get to be a better shooter and start thinking about upgrading, many shooter will let you try their gun. As the previous poster mentioned, don't try the Perazzis and Krieghoffs unless you have some serious money. Even if you can't buy them, they are fun to shoot.