snarzberry
Emperor
Build what first if gameplay is for Domination win?
Build what first if gameplay is for Space win?
Build what first if gameplay is for Diplo win?
Build what first if gameplay is for Cultural win? (And for this, I suspect Apotheoser is right)
Build what first if gameplay is for Points win?
Build what first to keep your options open (or is that really an option at higher levels)?
And.... do certain types of maps or starts change the answers?
Certain types of maps and starts definitely change the answers. And in response to your question about if keeping your options open is really an option at high levels I can say that it is in some situations, I'll give an example.
It's better if you ask a different set of questions. Based on what civ you are, what you can see of your surroundings and what neighbors you know of, then what first if-
gameplay is to remain at 1-2 cities, build up a fighting force and puppet enemy cities?
gameplay is to expand and settle new cities of my own?
gameplay is to remain at one city and aim for a peaceful victory type?
These are more broad questions and pertain to multiple win conditions, even on deity. For instance, let's say you are Mongolia and you roll a start with good resources and hammers. You decide, wisely, that the best way to proceed is to get an army of keshiks into the field as soon as possible. No alternative will reap more rewards than this plan well executed.
You can field an army of 4 keshiks (soon to be supported by a khan) and a melee unit by turn 80 if things go your way. Let's say you then puppet your entire continent of 2 neighbor civs by turn 130.
You find yourself now in a position that many have claimed is non-existent in civ 5. That is, a flexible one. Since you have only your original city (or more likely a second additional city that you needed to settle or annex unless your capital is coastal with a 4 horse resource) plus puppets, a cultural victory is still on the table. As is every other win condition.
What I'm trying to say is that the better question is 'how am I going to go about setting myself up in a winning position?'
For instance, in the puppeting army scenario, I would start with scout-monument-granary, with the intention of rush buying the library and having the NC built by the mid 40's.
If I had decided to expand as fast as I could to grab local resources then scout-scout is on the table as an option depending on the map.