Bludgeon and Eviscerate the Newbie

There are seven basic buildings that every city needs: storehouse (and later warehouse), library, mage tower, marketplace, consulate and barracks.  You will upgrade all of these buildings to level 20 with the possible exception of the storehouse, which only needs to be upgraded to level 15 in order to unlock inventory management and permit construction of the warehouse.

All cities come with a paddock and common ground in place; these should be upgraded to level 1 within the first week of play.  Common ground should eventually be upgraded to level 20 in all cities; paddock should be upgraded to level 20 in most cities, unless population is a constraint.

All first cities will need a tannery and a saddlemaker to produce leather armor and saddles, respectively.  These buildings may be omitted in later cities because it is difficult to keep up with production of both armor and saddles given the limitations of the common ground.

Players building their first cities will also want a spearmaker, brewery and tavern.  These do not need to be upgraded past level 1 (lev 2 for the tavern) until the city is fairly mature.

A bookbinder is useful to have in a first city, enabling one to build a few books if one has been hit by thieves and needs to reset a rune, for example, or produce books needed for diplomats.  The library should be upgraded to at least level 10 before building a bookbinder; you will need all the research points to do basic research before then.

Altogether that adds up to 19-21 buildings that are must-build for a new city.  This gives you some space to experiment with city specialization; some of the buildings may be demolished as your city matures.

Edited to add:  Architects Office is highly recommended for new cities; it can be built in a first city as soon as resource production is adequate to support a building program, at around 100-300 production of each resource per hour.  It can be demolished when other buildings in the city are complete and replaced with another tier 2 building.

Not sure if you read the whole post.  I mentioned the fact that elves don't use plate in my discussion of the forge.  

With regard to the kiln, Ryelle is an elf and has not yet had a need to build a kiln in her 3-clay city.  It depends on the tier 2 buildings one eventually wants to construct, but even for elves a kiln is far from being a requirement due to the low need for clay in general.  Building a kiln in a 3-clay city is probably not a good strategy anyway, since it results in lower production (since it's only boosting 3 clay squares.)  It is likely better to build another city on a square with abundant clay or as you noted to Exodus to a square with more clay if one wants to build tier 2 buildings with high clay upkeep.