Because of the low voltages, I would use synchronous buck converters. That are converters where another mosfet shorts the freewheel diode to reduce freewheel (catch) diode conduction loss.
When converting from 12V directly to 1.8V, you get short high current spikes at the 12V supply (as the switch current in a buck converter equals the output current). There can be an EMC advantage by feeding the 1.8V converter from the 5V converter, however, you may experience instability at the 5V output. This is because of the input of switch mode buck regulators shows negative resistance. So when using cascaded converters, check the behavior at all possible load situations.