1.2V, 3.3V, and 5V small power supply design
You haven't mentioned whether you need a fully enclosed solution, but if this is for a prototype I would go the following route:

Use a 110V/220V to 5V adapter. These are very common with USB output and their current output is typically 1A or sometimes more.

Unless you have very sensitive circuitry, use a Buck regulator to go 5V to 3.3, and then use the 3.3V to go to 1.2V. Avoid using LDOs when possible because they're inefficient and will dissipate a low of power.
You're doing good in attempting to reduce the input to output voltage difference (it is a big factor in LDO inefficiency if you go that route).

TI, Linear and others make combo devices that will give you a small solution.