The sad truth about Civ BNW final release is that game balance is extremely shifted towards peaceful tall empires (few large cities). Therefore you should always go for tradition and think about other policies only when that tree is completed. I cannot imagine an immortal/deity game with an opener other than tradition.
Furthermore, liberty should be only considered if you will be able to have a strong religion. You will need some bonus happiness per city. It's an absolute must. If you are able to have your religion very soon, go for pagodas. If not, go for happiness from temples. If both of these options are gone, keep going for happiness, ie. shrines or mosques. Underestimated cathedrals are surprisingly good for wide empires because they allow to store artifacts without bothering with both opera houses and museums for a very long time.
Start with tradition and if you can, finish it (you "cannot" finish tradition if you lack happiness to make an actual use of its finisher). Then go for some religion and liberty. You want cheaper religious buildings and reduced culture cost for social policies asap. Never finish liberty tree because it's simply not worth it. +1 happiness for connected cities can wait and bonus for settlers is a complete waste of resources. You've started with tradition so your capital is capable of spawning a settler or two every now and then. Buying them is also a good idea. You also don't need to finish piety, certainly not in early eras. Gold bonus for temples and great prophets' improvements has better alternatives and the only really useful reformation belief (worth spending a policy) is jesuit education. Unfortunately, the belief tends to be claimed quicker than a nubile cleric in catholic seminary, so it's just one another circumstantial factor.
The rule of the thumb for me in case of wide games is that I go for it only if I can secure pagodas or both bonuses for temples from my religion. That's because you must compensate for science and culture penalty for building additional cities.
If you really want to go for it, make sure to beeline radio. You can even bulb a scientist to get it earlier. The moment you start order, all your problems with happiness will be gone since this path will offer you almost instantly a total of +5 pretty much free happiness (+2 monuments, +2 factories and workshops, +1 universities) per city. This bonus will be increasing with time.
There's an alternative for religion, though. One of honor policies (I never remember names of any of them; I just click on the icon) offers +1 happiness and +2 culture for a unit stationed in city. If you couple it with free garrisoned units from tradition, you have an extremely cheap "building" with great yields that can be "build" the moment a city is established. Culture bonus from honor vs barbarians will help with early policies, though it's completely negligible since medieval era.
It's pretty obvious that wide strategies should be attempted only with religious civs, or my personal favorite, Poland.
Edit:
One more thing, a little remark directed at DarkestOnion's approach.
In GnK, you wanted to settle every tiniest speck of land before AI could manage to do so. In BNW, even when going as wide as possible, you will never want to settle the worst pieces of land. Science penalty is just too big. And what is usually more important in earlier game, luxury resources tend to be clustered. Large network of cities in early-mid game in GnK meant that you have a lot of luxury resources while in BNW usually means that you have a lot of copies of a few luxuries. It's a must to settle valuable spots, deny your opponents strategic location, but still remain rational with settlement policy. There's also the new-found importance of seas and oceans. In GnK, i hardly ever had naval cities, while in BNW I tend to pick worse but naval locations. Naval trade routes are simply too good to give them up. Also, consumption of early writers is usually a huge no-no for me because there are many turns ahead of you and by using your early writer this way you are giving up on 3 things:
1) border growth;
2) ongoing, cumulative culture bonus that will soon be higher than the immediate bonus;
3) tourism.
I tend to torment opponents in multiplayer with my tourism, even when I'm not aiming for cultural victory. Thy just neglect this aspects of the game and end up as my puppets. They follow your ideology because they have no other option, and you promote some other ideology to be the world ideology. You get diplo bonuses, your opponents are severely hurt, and the penalty you get yourself is negligible
).
