Despostism is great for early game expansion and warfare. Cities aren't penalized for units until they exceed city size, settlers cost 1 food, units may leave home cities for as long as they want. I expand with my settlers whilst sending out my chariots to conquer and settle my island/continent, whilst only building granaries and temples, using a 60/40 tax rate. My capital city has the Colossus to bring in plenty trade (and if possible Copernicus Observatory in the same city). Each new city builds 2 or 3 settlers, 1st 2 immediately build more cities, 3rd develops squares.
I generally switch to republic as soon as my island/continent is secure. The extra trade is awesome, warfare is still possible as the away units only cause one unhappy citizen which can be offset by luxury rate of 20 or 30 (JS Bach Cathedral also helps). The resource cost of units is annoying, but the extra resource from mines and special squares offsets this if you limit your army to 3/4 units per city. I can still conduct war under Republic, Democracy just puts red tape around military campaigns. Railroad enhances everything for republic, the capital city with colossus & copernicus & railroads pumps out technology. Womans Suffrage changes things for me. I now consider Democracy to be viable, where as before the 2 unhappy citizen penalty per away unit would hamstring my expansion. with this wonder, Democracy is Republic without corruption.
I view monarchy and communism as pointless, the increased resource output is nullified unless you have 1/2 units per city. NO EXTRA TRADE, which for me is massive. You do have increased food output but Republic/Democracy offers the same plus double the trade.
I know everyone has different styles and opinions, but we all find what works for us after a while.