Normal? Endless? Somehow I think it's hard to enter the contemporary era within 300 turns at the normal pace (metropolis difficulty), IDK it's me who don't know how to play it properly or it's just the normal pace. My playstyle is mixed, main scientist or merchant, with some militarist if needed. 

Every game so far for me has been normal speed at metropolis difficulty, Every game that I've started with Babylon and took up industry cultures after that with maybe a merchant for era 3 or 4 I've had to problems reaching the Contemporary Era. However I wouldn't count on reaching it if I went with something like a full Nomadic layout for cultures, also I've had easier times on larger maps with lots of competitors since the bonuses from trading resources add up quickly in a bigger game. Again this is all just personal experience, can't speak for others.

I always play 4x games at the slowest possible game pace to extend technology and to make every turn more impactful in the long run.

Might take me a whole lot longer to finish games but it feels more rewarding for me. All of my multiplayer games with friends are also at the slowest pace!

Initially, I went for very fast games, 75 turns, 75 minutes or so, but then I found out I like to finish a game within 1-4 hours within any given day, not too short or too long.  Therefore, at an average pace of 150 minutes & 150 turns (fast) seems appropiate for me, spending about a half a minute up to two minutes on a game turn, making it interesting.  Normal pace 300 turns would extend onto the next day, where usually I'd rather start a fresh than continue after a day old game, or it would be an 8 hour job in a day, I feel.  I haven't tried multiplayer though and wonder about time limits per turn and turns per day, as well as any breaking pts for other called for activities, like a 10 minute bathroom pass pause button informing other players as well.  I imagine a 600 turn game would take a week for those with the patience for it.  Maybe in a 600 turn multiplayer game, 100 turns a day would be a fine multiplayer setup for such a long campaign, with a time limit of 2 min per game turn, pressing End turn when rdy.  It would be Monday thru Saturday at the same time.  If someone is tardy or is a no show, then instant battle resolutions for them, and keeping the status quo or playing with/against their persona (I like that idea).

I've been going back and forth between slow and normal.  I think slow works a bit better for me.

I like the slowest pace because I want... to ENJOY the game. I'm not racing to finish it. I have fun in the journey, not the destination. Therefore, i want more time in each era.

I want to actually use the units I develop in each era. For that I need more turns. Since unit speed is unaffected, when you have more turns, it means you can march and fight more (also explore). In Civ, you never get a chance to actually use the units in the era you develop them because it takes so long just to get to the enemy city so I use a mod like 4-6X slower. Here, the current slowest setting is OK, but I can still finish a full game in 1-2 days.

I only play on the slowest pace, too.  Like the other posters have said, it helps me enjoy the game more and it makes me feel like every decision matters.

And specifically it gives me a long time in the Contemporary era.  The game changes enough in that era that it is more entertaining to have more time in that era.

300 turns standard speed with no endgame conditions except turn limit and pollution.

Blitz, if I just want to actually get to the fun part.

Normal, if I just want to figure out the correct way to play.

I haven't played fast or slow or endless, but I hope to test those out once I feel like I'm in a comfortable place in knowledge about this game.

I have played on Endless for the most of my playthrough since beta, when I'll feel comfortable with  s p e e d  probably I will try Blitzkrieg.

I can tell pollution is very annoying, AI just spamms upgrades that spread it and the game ends way before the end turn... Hopefully it gonna be fixed.

Slow at the moment, but probably going back to endless again. Sometimes it's a bit of a waiting game in endless-like game speed, but you actually get much more out of each period in my opinion and usually spend most time in contemp, which means you can actually use all these fancy buldings / weapons etc, so long pollution doesn't destroy your weeks spend on one play through out of nowhere...