Electrical – use a 110 V GFCI outlet on a 220V service

I'd use 12/3 -- that way, the neutral is there if you need it (for built-in outlets for instance), and you can use standard color codes. (Just about ALL /2 NM is black/white/bare.)

You can't step down 220 volts by using two live wires - that voltage is between phase and neutral and the voltage between phases will be 380 volts, so no cheap 220 volts is there.

Note that besides different voltages there's 50 Hz versus 60 Hz issue - your country likely has 50 Hz mains and if you use an ordinary (not switching power supply) transformer it can't get 60 Hz out. If any of your devices are for 60 Hz the problem gets worse.

You certainly can use the transformer and separate set of wires scenario, but...

1. that's a separate set of wires and breakers and junctions and everything - you need to find place for all that, install it and maintain
2. if the transformer happens to be too small you'll have to either replace it (quite costly) or set another one and another set of wires in parallel (quite complicated)
3. you now have two sets of outlets with different voltages across the house and if you plug a 110 volts device into 220 volts outlet it likely breaks and maybe starts a fire. Even if you have two sets of outlets such that they require distinct receptacles one can always use an adapter and plug into the wrong one. In general this is why two sets of outlets with different voltages is quite a bad idea in real life. Every time there's an outlet with voltage different from country mains this problem arises, the only real solution is to have the same voltage everywhere.