Civ V vs Civ IV Great People:
Anyway it seems that you have the same problem as I had with the great people. One of the few things which is better in CIV5 is that great people generating is not any more luck dependent.
I agree that non-random generation of Great People in Civ V is a clear improvement over random generation in Civ IV. I honestly can't think of anything else that is a clear improvement in Civ V over Civ IV.
Please excuse my off-topic comment.
To bring it more on topic:
Great Wonder Spam "Strategy":
I strongly suggest the Great Wonder Spam "Strategy". At Prince level, you should be able to build almost all the Great Wonders, except a few of the early ones. To help in this, make sure to select opponents that do not have the Industrious trait. Aim to build The Sistine Chapel as early as possible, spam all State Religion buildings (Temple, Monastery, State Religion "Cathedral") in the three Cultural cities. Each such State Religion building provides an extra 5 Base Culture per turn in BtS.
Don't forget to complete Great Wonders (including National Wonders) and cultural buildings as early as possible, since their base culture per turn doubles after 1000 years of game time. Try to complete as many Great Wonders and cultural buildings by 1 AD as reasonably possible.
War Chariot Rush:
At Prince level, an early rush can be very effective, since the AI starts out with only Warrior defenders. With Hatshepsut, you should be War Chariot rushing 1-2 closest Civs early on (before they find and connect Copper) to gain cheap REX. Choose opponents that do not start with Mining, since they usually complete Bronze Working much later and can't start building Gold/Gems/Silver mines very early either. Start with researching Animal Husbandry to locate Horse ASAP. You might try stealing a Worker(s) ASAP from one opponent that isn't too close to you and thus may not target you after Peace. Let your Capital grow at little and build a Settler to claim Horse (with the Creative trait, you can settle with Horse in Ring 2 which will be in your Culture in 5t) or claim Hammer heavy sites with enough Food to grow and support the Hammer plots.
Other Tips:
Workers play a key part in the rush, building roads to opponents, improving Resource and other plots, and especially chopping Forests. Try to get a start with greater than
average number of Forests which can be hard on Oasis; you might try playing a different Team # than the default of #1, if the map script always puts Team #1 in a Forest-less area of the map.
After Animal Husbandry, research Mining -> Bronze Working to adopt Slavery and chop Forests for quick Hammer boosts. After Bronze Working, the research path can diverge, but I like Pottery (Granary/Cottages) -> Writing (Open Borders) -> Mathematics (+50% Hammers for Forest Chops). Alphabet after Writing may be a better option to fill in the Worker Technologies and more.
Sun Tzu Wu
While the general Hall of Fame is an ongoing competition, we like to run time-definite competitions between updates that we call Gauntlets. Standard Hall of Fame rules (*) still apply, but any games meeting the settings will be counted towards the Gauntlet.
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that I have still not learned the lessons that babybluepants was trying to teach me back then: don't build axes and war chariots - just build war chariots!
. That accounts for the 2 Gt Prophets who got me the 2 late religions.
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. When did you get Liberalism?
). At least I used one engineer to rush the Shwedagon Paya as gold was extremely rare on my map (two sources). 
Do you know something about swapping the team number?! Is really there no means to swap team number?...so why people even bother mentioning it if nobody has ever accomplished it? 
