On your first turn, consider building a mine and increasing your population, getting a good start on resource production is a good idea.
Value resources over food. You can build a new farm with resources, but you can’t build a new mine with food. However, once you have built, say, a couple of mines and a farm, you will find that your population starts consuming food even if no new workers are created - this is not the case with resources. Also, the new workers that you need to operate the buildings that you build with your resources, and to man your army, become steadily more expensive, whilst the cost of the buildings and troops doesn't change as you build more of them (they become more costly from Age to Age instead). Be aware that there are not enough Irrigation cards in Age I for everybody to get one - not to mention that these cards might not appear until late in the Age - and without Irrigation you will struggle to increase your population more than once every other turn. Consequently, it is vital to make maximum use of other sources of food and population, e.g. Action cards and Events, until you discover whether you are going to be one of the lucky ones with Irrigation. If you are not lucky, you should consider a strategy that uses building upgrades to increase the productivity of the workers that you can afford, and think carefully about which Wonder(s?) to build, since these give you benefits such as happiness and culture points without requiring workers.
Don’t worry too much about happiness; as long as you have idle workers you can go without it. However, idle workers are a luxury that you won't be able to afford for very long - see above. It is worth having one, or even two, in Age A in case one of the Events appears that allows you a free build if you have an idle worker, but after that you are better off putting them to work rather then using them simply to compensate for discontentment. You can always disband them later if necessary; don't forget that disbanded workers go back to the worker pool, not to the bank, although it does cost an action to do it.
Don’t forget to take a Leader from every Age if the opportunity presents itself, but don't forget also that you can only take one Leader per Age from the card row, so choose one whose powers complement your general strategy; you could even take the first leader you see and let him or her guide your strategy - after all, the leader you really want might not appear till late. You get an action back if you replace a Leader before he or she becomes antiquated, so it will normally only be your first leader who costs you an action cube.
For most of the game it doesn’t matter how much stronger you are than your opponents, only that you *are* stronger. If you are weaker than your opponents, you will occasionally lose a cube or two, or miss out on the freebies from certain Events, but you should be able to make up for this using actions that your opponents are using to build up their armies. However, beware! In Age III, there are multiple copies of warfare Events that penalise you heavily for weakness; not only can you lose culture points that run well into double figures from these, but your attacker gains as many points himself, doubling the pain. So keep an eye out for 'free' strength points, that don't require workers, such as those from special technologies, Tactics cards, and Leaders (but there are no Age III fighting leaders, so you might need to plan ahead).
Michelangelo and William Shakespeare are extremely powerful for culture engines. Plan accordingly.
Saint Peter's Basilica is very powerful when matched with Michelangelo. The Great Wall is an extremely strong wonder.