I'm trying to run an ATmega48 off a quartz oscillator at 16MHz like so
Can't find anywhere what's the correct value to set the SUT to, or even what BOD means.
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BOD is "brownout detection" and mentioned several places in the datasheet (search for "BOD").
Above, from page 321, you can see that brownout detection can be disabled or set for different voltage levels. Brownout detection is basically a method by which the microcontroller will shut down "gracefully" in the event of low voltage. Depending on the application, various bad things can happen (memory corruption, incomplete carry-out of instructions, etc.) in the event of a power failure that is preceded by a voltage sag. Enabling BOD allows the microcontroller to record the reason for reset and avoid certain undesired outcomes.
If your application requires the MCU to reset and be operational very quickly, you would want to employ BOD and have the shortest start-up time. When using a crystal oscillator, for example, the minimum delay is 16 + 14 clock cycles. If you have to accommodate slowly rising power (e.g. >10 ms), the delay increases to 16 + 14 clock cycles plus 65 milliseconds.
For hobby use, it's generally a safe bet to use the longest startup time and not use BOD. Unless you know your requirements dictate otherwise, of course. The startup time is really only a concern when other components are interacting with the MCU and it is necessary to know, for example, how long to wait for serial communication or an ADC conversion or something in the event the MCU is reset.
Some additional information you may find helpful: