I realize I'm a few years behind the times, but I feel as though its time to move past Emperor level. King-Emperor didn't feel like that big of a step; I could still get a few choice early wonders if I started with tradition and had a productive capital. Is that going to likely be the case with Immortal? I know better than to try to string together 3 wonders in a row at this point. Which victory type is likely to be the easiest to come by for my first game?
Great Library : Forget about it on Immortal
You still have a good shot at any other 1 Ancient or Classical world wonder of your choice if you are willing to slow down settler construction during that time and start it early. But if you try a second ancient or classical world wonder after having finished the first you'll l get beat out.
Your choice of Stonehenge or Oracle (but not both in the same game unless you are Venice / or this is an OCC) is probably the most popular for humans on Immortal since these are right on the path to NC.
(There's others as well.) The least popular among humans on Immortal are the national wonders that are on techs that are normally deferred until after Philosophy. (The AI will probably complete those before you have the tech for it)
In BNW on standard map size with the default 16 city states, Diplomatic Victory is normally easyist. Standard Science is King tactics going into the Modern era, after a few key Modern era techs lay down a pure beeline to Globalism. Open Patronage to build FP. Use city state quests & spies to become allies. (Go Freedom and adopt the level 3 tenet that gives city state influence every turn with trade routes unless the World Congress has embargoed them.) If all else fails you can cash buy the remainder of city states the turn before the vote and then DOW all the AIs so they can't take them back during their turn.
Be prepared for a fallback should a large number of city states be removed from the game. (If the Mongols or Huns conquered them, you can liberate them, but if it was Venice buying them or Austria marrying them, their gone)
If you cut the city states down to a more reasonable level on Standard map size (say 8 for a 1:1 ratio), then basically the stars would have to line up perfectly for diplomatic to be fastest. (You must build FP, AI Venice must NOT be in the game, you must be able to liberate any city state that got conquered) This doesn't mean its impossible it's just that during the 20 turn delay following a failed world leader vote some other victory condition would have been faster if you'd gone after that instead.
The faster between Science & Culture for normal number of AIs on standard map size as a normal civ (one without cultural or tourism bonuses) is going to come down to what your hammer production of your capital will be when you reach Printing Press, which in your first game on Immortal you might not have enough experience to know. (That period of the game has most of the theming world wonders.) Presence or absence of some of the other AIs is also a factor. (Example: Seeing AI Egypt would be a sign to go after science victory instead of cultural)
On a map with more than 8 major civs, chances are high that scientific victory will be faster due to that more competition for those key wonders. Conversely, a map with fewer civs would make Cultural victory a shoe in.
Any of the "God Tier" civs is best for the first Immortal level game. (Poland, Babylon, Korea, Inca, Spain *)
* Spain is only at God Tier level if there is a nearby natural wonder that you are first to discover.