Regent level is easy to play even if you don't have strong military,
by using trades and exchanges human player usually outperforms economically and technologically al AI civilizations as soon as early middle ages.
When i mastered regent level i never tried to build any AA wonders (i know, i know there are some good ones i sure miss), but instead was building up economy and actively trading technologies and when middle ages come I have all the wonders to myself up untill the end of the game.
Situation changes at the monarch level and above (i never got above emperor myself though). I don't know how the rest but for me priority No1 is to be most technologically advanced civilization, i don't worry much about culture points and i am not a hardcore warmonger. But, if you want to be advanced on hard levels the only way to do is is series of short but successfull wars as soon as you get iron. By the time you get iron all civilizations around usually are way ahead technologically, so I just try to build pack of swordsmen (10+)with support of spears (4+), latter mostly to guard captured cities and then i attack neigbor. Make sure to check your military advisor to say that you have strong military. What you need to do next is to quickly capture at least 3 cities. Usually AI is willing negotiate peace after 2 of his cities are captured, but i found it's not enough. After 2 cities AI will make peace but won't give away much technoliges, so make it 3 and AI will give you everything he has.
Next step - you need to expand, and do it at the expense of AI. I rarely build more than 5-6 cities before i start. So after you made peace with first AI and peace treaty will last for 20 turns which AI usually will never break at AA (it's just nobody around has enough money to buy MA against you at that time) it's time to attack your second neigbor and since you sucked all the techs you don't really going after those, now we go after cities... Same tactics, capture 3 cities or 4 if you are strong enough (you were keep building those swordsmen, weren't you?) and then make peace and demand more cities, trust me AI will give you almost everything he has and this civilization will never be a major threat again. Now it's end of AA and you probably have big and powerful civilization, now it's time to switch to republic if you wan't to do some buildup or to monarchy if we want to turn back (those 20 turns of first peace treaty just expired, didn't they?) on the first AI neighbor and since he probably still has'nt fully recovered he will be an easy prey for total annihilation.
End of story, You will rule middle ages.