I generally agree but what you describe is a good commerce (cottage) city but not a good gpfarm...
If you are on a level that you struggle to win on (or have even and tough fights with the AI) then you can't win without it generally.
I find myself not looking for commerce and production but for GPFarm sites first. I suggest you try that too. Finding great commerce cities is usually easier than finding a great GPFarm. BTW
for big amount of planning early on
Now that's less good. Founding an early religion yourself takes away AI-AI tension (and can lead to "lovefests" where all (other) AIs love eachother due to shared religion; in these games the techpace is fastest). Also you generally shouldn't spend that many hammers in missionaries. Without missionaries your religion won't spread that far and your shrine won't yield you much.
Getting the shrine in a production city isn't so bad. It'll have market/grocer/bank/Wall Street up faster and can run merchant specialists to maintain 100% if possible.
Capitals nearly never get a religion. The more religion are present in a city, the less likely a religion gets founded there. The more pop a city has the more likely is it that a religion is founded there. I think this is it.
Happy civvin'