I suggest you to work on the input voltage side circuit. If you are generating DC from a transformer based rectifier, then use a 7.5-0.7.5 transformer and use it with a 7805 voltage regulator. There is no point in using a seperate regulator IV for the LED arrays. You can simply remove the LM317 circuit and connect the LED array directly to the output of the 7805 through a resistor of value less than 1K. It would be better if you connect each LEDs through seperate resistor 1K or 330ohm resistor, rather than using a common resistor.
You can use any N channel mosfet which is easily available, but to reduce the cost i suggest you to go for general purpose NPN transistors like BC548, SL100, BEL100N etc.