Huh. I didn't know about the 16 MHz. Well you learn something new every day.
FallenDemon:
So if I were to buy the Attiny85, what else would I need to buy to program it with my Arduino? Does the chip include the pinout diagram?
If you have another board like a Uno you can use that to program it. As Coding Badly said you can use the ArduinoISP sketch. I also show here how you can simply dump a hex file onto an SD card and program it from that: