Choosing a correct transformer for a power inverter?
How does one choose a proper main output transformer for a power
inverter? Is enough to simply use a &quot;standard&quot; transformer &quot;in
reverse&quot;?

This answer assumes that a transformer with a regulation factor of 10% is used. For bigger transformers (circa 100 VA or beyond) the regulation might be 5% or less.
It would be really nice if a step down transformer producing (say) 12 volts AC from an input of 120 volts AC has a turns ratio of 10:1 in step down. Unfortunately this isn't quite the case because transformers are not ideal and might &quot;sag&quot; the output voltage by 10% on full load. This means that a 120 volts to 12 volts transformer probably has a turns ratio more like 9:1 and, unloaded, the output will be 13.2 volts. On full load it will be 12 volts.
OK, given that knowledge about power transformers, using it as a step up device from an AC source of 12 volts RMS means that the unloaded output will be 109 volts (not 120 volts). And, under full loading conditions the output might drop to 99 volts.

do toroidal transformers convey any special advantages to inverters?

Not particularly, given that you might need to add 20% turns to the high voltage winding and rewinding a toroid (by hand) is a pain compared to a regular transformer (which can usually be dismantled).