The whole concept of city specialization is obsolete imho. There are only very few cities, that get specialized to mostly only one thing. The capital often is best as a Cottage city beacause Buro is so strong. The NE + GT city get farmed, and HE city is specialized to mostly Hammers, though Farms don't hurt either. IW city gets specialized to only Hammers and the NP city needs Preserves, but that's already all city specialization that takes place imo..
The standard, no-National-Wonder-city doesn't get only Cottages, only Farms or only Hammers, because it gets specialized differently. I always like to describe this as the way . If it's still very early, one specializes the reasources and the riverside land. If a city has Silks, that doesn't mean anything yet. If one goes for HA-rush or for Elepult, this city probably will get some Farms and some Mines to whip 4->2. However, after the rush, one will be in need for Commerce to support the conquered cities and to tech to the next military tech. Then, the same city will get 3 Cottages, improved Silks and one probably will build a Forge and a Library in it. This doesn't mean however, that those will be built over the existing Farms or Mines, no. One will be happy about those production tiles, because they let one get those buildings faster. One will let the city grow to size 8, and one won't whip it because those buildings aren't urgently needed.
Then, one will want some Maces or Trebs, to continue the war together with the left-over HAs or Elepults. That's maybe 1 whip and possibly two less Forrests.
Then, one will reach Education. If going for Space, this will mean, that one wants some Universities to build Oxford. That means, the six most powerful cities get chosen for this, not the six that have the best Commerce out all. Oxford produces more bonus-beakers when reached earlier, same concept for the GT or the WS.
So the size 8 city will now be whipped down to size 4. It will regrow on the same mentioned tiles, and Workers are still mostly chopping or they build Windmills on the Hills that are still left. This will allow the city to grow to size 10. However, then Chemistry gets into play and because the empire got large and because one looks forward to Corporations, one will want Banks and Grocers. These don't get whipped, because that would mean a lot less research, so one will build Workshops and Watermills on all tiles that are left.
Now the city has 2 Farms, 2 Mines, 4 Villages, 2 Windmills and the rest are Workshops and Watermills! The city produced 3 HAs, a Library, a Forge, 2 Trebs, 1-2 Maces or Muskets, a University and it's getting the Gold multipliers on top, even though it only has very few Cottages. It's still right though, because the city is large and powerful, meaning it 1. can produce large buildings like a Bank, and 2. It has strong TRs!
If you understood this post, you understand the concept of hybrid economy and you'll advance your play at least 1 level.
I could give much more examples, but I'm writing from a handy and I also already plan, to write a guide on this.
Questions you should consider, are, what improvements help me best now, again and again, and you should ask yourself, what will be the most powerful improvement now, and regarding builds, you should ask yourself what will benefit this city now and during the course of the game, but you should more so ask, which cities have the power to build now what I want, which cities are the fastest for a specific task.
I hth.