http://www.mpja.com/5M-Blue-LED-Lighting-Strip-12V/productinfo/19441%20OP/
The LED strings I looked into have 3 surface mount LEDs and a surface mount resistor, and can be cut into groups of 3. I attached the link to a blue string because they have a datasheet for it. That means that they need a regulated 12V supply to run at the designed current. Overdriving them with 120Hz pulsing DC won't result in long life. Your transformer, bridge/heat sink, should be followed by input caps and a fixed regulator like the LT1085CT-12.(12V/3A fixed) An adjustable regulator like the LM350T and 2 resistors would also work. Both require heatsinks, additional caps and diodes and a circuit board. In other words, you probably need to buy a listed supply, rated conservatively higher than 25W.
Joe