2 3/4 Dram Equivelent "Light Target Loads" are pretty much norm for singles, doubles, and short yardage handicap. Velocity is 1145 for 1 1/8 oz, 1180 for 1oz.
1 1/8oz for handicap, 1oz for 16 yard singles and both shots of doubles - you don't need more than that. For shot size, 8's are my choice for singles and caps, but 7 1/2's are good and I use them in the wind for handicap or during the winter. I use 9's for the first shot of doubles, and 8 1/2 for the second shot.
If you go back maybe 24-27 yards for handicap you may want to look at a 3 dram or handicap loads like Remington Nitro 27's or Federal Gold Medal handicap loads. These are rated at 1235fps.
For inexpensive stuff anything will do - 3dr "Wally world" value pack shells are fine...but they're usually 3dr eq, 1 1/8oz. I use any big three for singles (Winchester AA, Remington STS, Federal Gold Medal), Winchester AA's for doubles, and I find Federal Gold Medals best for handicap.
And finally, don't listen to "randkl" telling you to use "Super Sport, Sporting Clay" loads, for two reasons. A) you don't need them for trap, its all extra noise and recoil for nothing, and B) if you shoot registered you will be disqualified, because Sporting Clay loads exceed velocity limits and are illegal for trap per the ATA (and I believe the PITA) rule book.
ATA member, registered trapshooter
Local - State - National Champion (2007 ATA Grand American World Trapshooting Championship, Sparta IL, Category place, Yardage winner)