My first post! This site is fantastic! I wish I knew of its existence a LONG time ago!
It really depends on the city and what I feel it needs at the time. For my very first city, I'm looking to strengthen my military first so I build a Barracks and use this city as the source for my military units. Next, I try to build a temple to continue to increase my culture. I never build walls because if the city is growing rapidly, I'm usually at 7 long before I end up going to wall, thus defeating the need for Walls. For the most part, I don't bother with Ganary either. I usually just build a Pyramid. If I'm going for a military victory, Marketplace is usually next, otherwise, I go for the Library. Courthouse, I don't bother except for two circumstances. A) If there is nothing else to build or B) If the city is suffering from a high rate of corruption.