There are essentially just two ways of accomplishing AC dimming: altering the waveform's duty cycle, and altering the waveform's amplitude. Regardless which one you choose there will be devices which will not tolerate the dimmed power waveform.
Also, all dimming techniques involve some power dissipation inside the dimming device itself - thus the dimmer must be designed to provide the full range of power levels that it might be called on to deliver.
Old school incandescent bulbs will tolerate either type of dimming. As will any device that simply relies on the principle of generating heat from a current flowing through it. For instance, simple space heaters will usually tolerate being dimmed by either method, but require much higher power/current than most light bulbs.
Fluorescent lights will generally not tolerate either manner of dimming. Their ballast transformers and start-up voltage requirements generally rule them out for supply voltage waveform dimming.
Many LED lights are designed to accept either form of dimming. Some, especially older LED bulbs, might not. It all depends on the design of their built-in power supply circuitry. So check the manufacturer's specifications to be sure.
Most AC electric motors will accept some degree of amplitude adjustment without risk of damage. Ceiling fans, for instance, generally accept a wide range of AC voltage amplitudes. Vacuum cleaner motors are not necessarily so tolerant. That would be a consideration if you are contemplating providing dimming to a wall outlet for a floor lamp: you probably don't want to do that if someone might plug in an incompatible device in the outlet.
DC lighting is a different beast. With DC there is no waveform variation, just a voltage level that might be adjusted. But most DC lighting is designed to run from a DC voltage provided by a power supply that obtains its power from standard AC voltages. Depending on a DC lighting system's power supply design and bulb technology it might or might not tolerate AC dimming applied to the input to its power supply. It would be best to consult the DC lighting system manufacturer's specifications to determine how and whether to attempt dimming such systems.
Once you know what you are dimming, then your options will be narrowed. Regardless, there are likely to be options open to you that will not involve adding another processor, like the Arduino.