standalone MEGA 2560

CrossRoads:
Burning a bootloader using the IDE's Tools:Burn Bootloader also sets the fuses for correct operation. Do that first before loading any sketch, even if the sketch is to be loaded via File:Upload Using Programmer (after which the sketch starts after any reset, the bootloader is wiped out).

My process for programming standalone Atmel processors so far has been to use the AVR ISP II ($35) with the programming software included in Atmel Studio to do the programming. This will write the ELF file created by Arduino up to the chip over the programming port, and has a section for setting whatever fuses you want. In addition, you can use it with the AVR Dragon's ($50) High Voltage programming mode to fix bricked chips. In addition, if you want to use Atmel Studio to actually write code, either programmer will allow you to debug your code running in-system, which is great.