What difficulty and game speed are you using? That start is not a common build order. Generally, people go scout, scout, shrine, settler (sometimes granary) and at earlier difficulties, you may need a worker in there. Archers aren't typically built until later, unless going for domination.
All cities should grow and all cities will get granary and library early. If both can be built in time for NC, you build granary first, but if you can't build both before you are going to be starting the NC, then you'll want to build or buy the library first.
After that, then you will generally build all education stuff in all cities. Market, banks and so on, will go in cities with good gold production, but can be built later in cities with little gold. You should also have 2-3 cities that have production buildings, but if you have time in other cities, there is no reason not to help all cities get production, as it helps you build your buildings faster.
If you are going for a domination victory, you will likely specialize a couple cities to build units with military improvement buildings, but do not bother building them elsewhere, unless you going after a national wonder.
