If you're on Emperor, then you *can* try and get the GL and beeline straight to Philosophy for a quick NC before you get your multiple cities up. The key is growth, and production comes in play later. You should try to get the most out of Rationalism as early as possible, get PT and start spamming RAs. Around the time you get to ideology, you may not be able to choose what's best for your finishing time, but what's best for your survival because if you're going for a SV you're likely not be able to churn out much tourism and your own culture will defend you only for so long. In G&K it was almost mandatory to burn a GE to get PT just in case, but in BNW I use the GE to rush Hubble, which if you did get, pretty much secures you the SV. Be warned, you *may* not need to burn GE for that but you never know.
If you're going Freedom, there's no need to rush the level 3 Tenet, especially if you're having happiness issues. Focus on that and growth. If you're going Order, the science bonus from factories is really good to have but again, no need to rush past that. Either way, you need to time your free techs/spies to get the ones you need as soon as available and then use your own science/RAs to level out the tree. You get free techs from Oxford, Rationality finisher and whatever your spy can get. But that last part is meaningless if you run away with your technology.
Don't plant your GSs either, maybe one or two, but save the rest (you should have at least 5), to get the last part of the tech tree
As for the culture strat, here's what I did:
Settle cities quickly, get those guys out while there's land to be grabbed. Then try and grow them as much as your happiness allows, and make sure you get NC early. Getting a religion up is also good but more often that not, you'll be late for that party, unless you hit two religious CSs and a pantheon just appears out of nowhere. Around that time you should max your GP modifiers and have both the Writers and Artists generated. Naturally, save them for when you align yourself with the era you want to make the most of. However you need to plan ahead with your Wonders, because if you get Uffizi, Sistine, Louvre AND Hermitage, good luck getting the bonus out of all of them
I also had 2 GEs saved up, one from Liberty finisher and other from Pisa, naturally I used both to steal the wonders my spies saw were being built :]
Policy-wise, you need Secularism from Rationalism and then try and finish Aesthetics. With a culture game going, policies will come out more quickly and if you have Globe Theater and Oxford both filled out, the only need for GWs is to burn them for more culture. In one game I finished Exploration for hidden sites which I used for free GWs, I burned through the tree so fast, I had to pick useless freedom tenets because I already finished all policies I needed. Make sure to win World Fair even if you're not a religious civ. Around the same time I had national visitors center, International games and Internet finished and that blew my tourism off the charts. The rest was just faith bought GMs bombing all over the place