Thank you all for your advices, but I expected somewhat different.
I already figured out that I should have gone rapid expansion with Liberty, so what I wanted is a step-by-step build and reseach order variations.
I can't comprehend how Honor/Warrior rush will be successful above Noble.
Samurai rush is what I actually did. Ended screwing it up though.
Rapid Expansion via Liberty is fairly straightforward. I am going to assume here that you don't get any Culture ruins, El Dorado gold, or any other large early benefit. I am also going to assume that your map gives you enough elbow room to settle 7+ cities with aggressive blocking (if not, you need to attack early or turtle up for a renaissance war).
REXing is unit-intensive in Civ V. You will be building units and not wonders or many buildings. The goal is to block the AI and claim the good city site early, while dealing with the diplomatic repurcussions of settling near your opponents. You want to settle a LOT ... if you just settle four cities, you're better off with Tradition. Liberty shines with lots of cities. The key is to keep up your military and get as many unique happiness resources as possible, understanding that some of your blocking cities may be suboptimally located for strategic reasons.
Social Policies: Take all of Liberty, excepting only Republic, which may possibly be worth taking depending on the land you have (+1 hammer per city sounds lame, but consider that in the early game, this is like a global +10-20% production bonus). When you take Meritocracy, try to get the most bang for your buck. Since you are REXing, a settled Great Engineer will do wonders to improve your capital's hammer output, although rush-building a wonder is tempting (many take the Great Library to deny it to the AI, get the +1 culture per turn, and still get the free tech (Civil Service?) that a great scientist would have granted). I have also taken a great merchant and done a trade mission to secure the alliance of a friendly maritime or cultural city-state that has a luxury I need so I can keep expanding. For the really land-grabby, you can take a great artist and culture bomb a nearby city state to take its precious unique resources away and give them to you. Just remember that every happiness resource you get essentially lets you settle another city.
Tech order: Pottery, relevant happiness resource techs, writing, philosophy (temples and research agreements), a few relevant military techs (archery, BW, HBR, IW), construction (for coliseums and lumbermills)
Build order: scout, monument, granary, worker, warrior, settler (repeat last three until happiness causes problems)
New Cities generally get a monument and granary first. You want every city to have a warrior garrison at the beginning, when barbarians are an issue. Your city ranged attack and warrior will be able to deal with barbs. The bigger threat is the AI you just blocked. Eventually they will come at you with whatever they have on hand ... several warriors, possibly a spearman, an archer or two, and a horse or two.
Use your cash to buy tiles to block off the AI. I can hear many of the Civfanatics playerbase screaming as they read this. Do it anyway. You are trying to secure territory for yourself to expand into. Hook up your cities with roads, using as few road tiles as possible to save on maintenance. Research agreements are great but not the centerpiece of this strategy. You are trying to maximize your land grab here.
Happiness buildings will become necessary as your cities start to grow vertically. If available, build Circuses where you can; although they only grant +2 happiness, they cost no maintenance. The other happiness buildings will eventually need to be built as well.
Eventually, you will have to go outside your empire for more happiness -- trade with AI civs, alliances with City-States, and Piety and/or Commerce are likely choices. Piety, in particular, has nice synergy with a REX strtategy, as Theocracy grants a 25% unhappiness reduction for all settled (i.e. non-conquered) cities. Thus, if you have eight equally sized cities, you are getting two for free, happiness-wise. This lets you settle two more cities! Depending on your map and gold situation, Patronage can give you great culture, food, and resource gains in exchange for substantial regular gold infusions.
I hope this helps. REXing is great fun but you have to stay with it and remain focused on new city expansion and happiness. Once the easily-settled land is gone, you will find yourself with a huge population and resource advantage and in great position for any of the non-cultural victories.
