Until unit supports matters warriors are the better investment due to their slightly greater combat power per shield. Babylon is the example where the UU is actually on par with warriors.
Unit support can matter quite early if you go for many warriors. At 10 shields per unit you donnot need much production for that. There are instances were a warrior rush makes more sense than an archer rush, but those instances are few.
I can't say I've ever done a warrior rush outside of Jaguar Warriors or grabbing undefended towns at lower levels (it really doesn't happen once they do the settler/spear thing). I guess if you had numbers and the AI had only warriors defending a town you needed RIGHT NOW it would make sense, but I haven't seen such an instance myself.
I was more thinking about Sid: You need war very early because else you will have a hard time grabbing enough land to become competitive. So yes, you might loose say 10 regular warriors per town you attack, but in despotism that is not that much of a price if the strategic objective warrants this expense.
Given that Sid AI have all the starting units and lots of spears, seems pretty rare? Would love to see an example of it!
For it to work well you need the target to be involved in at least on other war. So you may well need writing and an embassy. This competes with aquiring the techs needed for spears and archers. You may start with alphabet, research writing in 50 turns with minimal research and as soon as it seems convenient war may commence.
Hitpoints. So veteran compared to regular. Barracks that early in the game are usually not worth it.
No:
Yes.
