Ok, I'll accept.
1. Should we prioritize production or growth?
2. What should take priority, connecting cities and luxuries of improving terrain?
1 - This is a 2 part question.
a. In the beginning, food is king. At 5fpt, a
granary (remember this from games past?

) and about 6-7spt, we can have ourselves a 4-turn settler factory.
b. Once we have an established settler factory, cities can be assigned as settler, worker, growth, military, or wonder/improvement cities. I include "growth" because of C3C's corruption model. Due to the new corruption model, there will be many cities that will have massive corruption. If these are floodplain cities, then we can assign specialists (scientists, taxmen, engineers, policemen, etc.). Production and growth all depend on what your goals are. Interior cities, once the expansion phase is over, will be production cities. These will be maxed out in 5s, 10s, 15s, 20s, 30s, etc., so that minimal shields are wasted. Corrupt cities, on the other hand, can use the specialists (which are much more powerful and useful in C3C - I once had 4 turns of science research on specialists alone!).
2 - Was this supposed to be an "OR" statement? If not, then the whole statement is true. *jumps out of programmer mode*
connecting cities and luxuries of improving terrain
I'll take this to be:
connecting cities
or luxuries
or improving terrain
Cities - Yes and no. Priority should be building the road to the next city site. That way, our settlers get out to the sites faster. Roads are like the rails of the ancient era (thus why LKentdar uses a rail-like road graphic), and should be best used for expansion. Workers are limited at this stage, so you need to balance out agressive road building with improving terrain.
City priority --
1 - Building a road to the next city site. Only a rigid rail-like net is needed.
2 - Building a road to a city with a harbor/airport (i.e., a weak city on an island). This helps to get the resources there.
3 - Interconnecting cities. Once the terrain around the cities are improved, then we can go and create other shortcuts, if needed. The exception would be in the planning of a "War Road" to let our troops go to another civ quicker.
Luxuries - Early on, not high on my list. If we have 1 luxury nearby, then great, we'll build a road to it. Early on, we should be keeping cities under size 6 for workers, and settlers. If we need happiness, temples are a good substitute. We should concern ourselves with 2 luxuries at the most before our cities start going past size 6. If we have ivory, then great, that's a bonus. That would be a high priority (For the Statue of Zeus).
Luxuries Priority --
1. Getting one or two luxuries early on is ok.
2. Once cities start hitting the size 7-8 mark, luxuries #3 and 4 will be needed. Markets also play a big part in this too. Once markets near, luxs #3 and 4 will also be connected.
Resources - Didn't see this one in the list, but I'll add it in. Depending on if we're planning an early war, this on varies in importance. Horses are good to have early just incase a civ were to attack us. We'd have some resource that doesn't deplete.
1. Non-depleting resources - Horses would be #1 to connect. My view is that, it's better to have something early on that you can continue to build without fearing the resource will deplete.
2. Iron - If we want an early sword rush, or horses are really far away, then this would be #1. If we have more than 1 iron source, then it's a bit higher. Other than that, it'll be connected when it's really needed.
Imporving Terrain - Each city only needs about the same number of tiles improved as its' city size, plus one for growth. Interior cities will have the higher priority to reach its' spt goal.
1 - Mining. In despotism, mining is the only way to go -- exceptions are bonus food. This gets our cities to the spt level that we want.
2. Irragation. this is only used on bonus food tiles, and plains/desert. (desert
may be mined if enough floodplains are available).
3. Roads. Since this is emperor level, I'd rather focus on the mines/irragation first, especially if the bonus grassland happens to be across a river (making a road pretty useless early on). I would focus on roadbuilding next to rivers first (with unobstructed movement), then other river tiles or gold-producing luxuries, then all other tiles.
This would be the general worker order that I would use.
1 - Look for bonus grassland tiles/food tiles along rivers first. Irragate (or mine), then road.
2 - Once the first city is improved (about 4-5 tiles before the settler factory kicks in, if we have one), build to the next city site. If the city site is divisible by 3 from the origin site, then don't bother building a road there, since the settler will stop there anyway.
3 - In the meantime, get some more workers (2 for industrious, 3 for non industrious), improve the surrounding terrain of the new city, and build roads to the next city site.
4 - If possible/needed, connect any luxuries/resources. Not high on the list, but if we have a fast growing city, then we might need one or two. Connect a strategic resource early on if military wants an early war.
5 - After the expansion period starts to come to a close, build the cities up to a desired spt value, and connect any remaining luxuries.