The strategy section is rather verbose and not all advise are productive. I am reworking it section by section.
Here is the old Dynastic Circle section for preservation.
Care should be taken to leverage your improved boosts that chop 20% off the time it takes to complete a boosted civic/science compared to your opposition. The improved boosts don't work well with the early use of Campuses or Great Wall, because then you'll get more sciences/civics before you can complete the boosts.
Inversely though, if you focus on structures and great people that give random boosts to your Eurekas and Inspirations, this ability will trigger along with those bonuses. Wonders like the Great Library will benefit from Dynastic Cycle.
The First EmperorEdit
The obvious exception to leveraging Dynastic Cycle is Astrology. With builders contributing you can easily beat every other civilization to Stonehenge (presuming that you have access to Stone) and get your pick of the beliefs (of which Divine Inspiration will further accelerate your Religion start), so it's not a good idea to wait for a natural wonder before heading for Astrology. Religion will become a significant part of the game and a huge head start on that is too good to pass up. Mahabodhi should be a priority not too long later (assuming that you've placed your holy site next to at least one woods).
Other wonders should be built quickly as they become available and making some of them available should be prioritised. The Pyramids should be an early priority as it will accelerate your other wonders and improvements, paying for itself many times over, so any land within 3 spaces of a desert should be considered carefully as a potential city location.
(Below is largely untrue as of Winter Update 2016. A builder loses all movement points after charging a Wonder.)
Further Wonder AccelerationEdit
Serfdom is a policy that adds 2 uses to each builder completed with it active. Once you acquire the Feudalism civic Serfdom should be on most (if not all) of the time until you've exhausted the ancient and classical wonders. With the Pyramids this allows a single builder to complete an ancient or classical wonder in 7 turns, 6 if your city can manage 10% of the cost in 6 turns. Note that if you're in no risk of losing it in that extra turn you should use 7 builds for each Wonder as even 10% of any Wonder is still worth more (in  Production) than a build. However, to use the build on the entire 10% you'll have to micromanage for a few turns, ending each turn with the city not building the wonder, i.e. only switching to building the wonder for long enough to spend a build and then switching straight back to something else. I'd probably disable auto end turn for the duration.
To make the process even faster if you think you're at risk of losing it you could tailor your builder use to the terrain:
|Movement Cost 1 Terrain||You'll be able to finish faster with multiple builders, so long as you've left less builds on a builder than it will take to complete the wonder, because in a turn in which a builder uses its last build another builder can take its place and use one of its builds, resulting in a turn in which the wonder progresses 30%. You could finish a wonder in a single turn, but it would take considerable managing to do so and you'd almost certainly have to lose some resources by leaving terrain unimproved for at least slightly longer than it would have been otherwise. The key would be to leave a single build on each builder except the last.|
|Higher Movement Cost Terrain||Using multiple builders will slow the process down, as you'll lose a turn after each builder moves onto the tile. Note that this will only apply when the following builders have to embark or disembark to reach the tile, as land based wonders add a road to the tile when you start building them.|
An additional bonus to consider is the policy Ilkum (in the early civic Craftsmanship) that reduces builder cost by 30%. The policy by itself actually adds more to the efficiency of The First Emperor's wonder rushing ability than even the Pyramids do. E.g.: For a Classical Era wonder that costs 400 hammers, a Builder costing 56 hammers will consume 240 hammers of that cost over 4 turns, meaning for every hammer put into a builder with the 30% reduction in builder cost, you get 4.28 hammers out of that in Wonder rushing.