Since the update of March 13, 2012, you get a "free city" (you don't need to spend purified resources to research title advancement) for every castle you own. To take advantage of the free title advancement, my second city is a castled city. WARNING: CASTLING YOUR CITY WILL SUBJECT YOU TO SIEGES AND ASSAULTS. This is a risky move if you are not in the dominant alliance of the continent. Even then, it is still possible that you get attacked or even loose your city.
I want to take advantage of the free title advancement, but it's very difficult to build a full castle at this point. I don't have enough iron and stone resources, building a full castle will slow me down. So my second city is a "pseudo" castle. A hybrid between resource and military. This is the only time I will recommend this type of castle. Other than this city, you should always build full military castles. A full castle packs a lot more punch! My second city is a mixed resource city with about equal wood/stone/iron/food (use auto city planner for this.) I also build a cluster of military of 2 training grounds and 10 barracks. When I have enough purified resource to research for my 3rd city, I will also castle this second city and found my third and fourth city at the same time. [You may want to wait to castle your third city instead of your second city, but you will not be able to found your 3rd and 4th city at the same time, which can slow down your growth]
This is my actual second city in world 83. http://bit.ly/SFWxBU