You can write your sketch using the Arduino IDE and then upload it to your chip using the "Upload using programmer" menu option. You need to download an extra driver to use the AVRISPmkII with the Arduino IDE (sorry, I can't remember where I downloaded mine from).
A virgin atmega328p will have the clock set to the internal 8MHz oscillator with a prescaler of 8 (so 1MHz clock frequency). To use anything different, you will need to program the low fuse byte. The easiest way to do this is to use AVR Studio and your AVRISP. Two warnings:
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Be very careful with the high fuse byte, one of the bits in it will DISABLE future programming via ICSP if you get it wrong.
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Once you set the low fuse byte to use a crystal, you can't then program the chip unless you have the crystal in place or you apply an external clock signal.