I gotta agree with Ming on this one with a few added points.
Single Player it really doesnt matter.
MP it all depends on the settings. In addition you can't count on getting a specific wonder so my strategies are based on no wonders. If I get them they augment the strategy.
1x1x deity you almost have to go Monarchy first or your expansion will be severely limited. Exceptions would be a high food/high shield start for 2 or 3 of your early cities.
At the other extreme 2x2x king. Almost always Republic first while building horses and settlers. Get the cities to size three WLT*D them to 8 quickly. Unless you are surrounded by a bunch of warmongers then I take the 8 tech path to chivaly, then go for Republic.
2x1x deity is probably the level where, at least for me, it is about 50-50 which I go for first. In those games it depends alot on the terrain, other players styles and wonder likleyhood. From my experience with the people i play with at this level, most go for monarchy first, but certainly not all.