Clint, I am surprised that you can start the same way every game. What if you start close to a few wheat squares? This will mean that you produce more food and less shields than if you work bonus grasslands. In my games, this would lead to the first settler built sooner.
Furthermore, I think that with your tactics you will be outsettled by the AI with a great margin if playing above regent, so I guess this is on one of the lower difficulties.
For the record, my initial play depends on the terrain. If not playing expansionist, I usually produce as many warriors I can while making sure that the first settler comes as close to size 3 growth as possible (usually the same turn). This normally means 2 or 3 warriors before the first settler. Then, if the capital seems to be the main settler producer (wheat/cattle/flood plain), I will try to get in a granary and then settlers as fast as possible.
Generally, in the early game, my cities falls in one of four categories:
* Settler producers (close to wheat/cattle/flood plain/wine).
Get a granary pretty fast and then settlers with the odd warrior if needed while waiting for the city to grow. Temple or barracks is quite low priority here. A worker will be built instead of settler once in a while.
* High production city (close to the capital, with many bonus grasslands, some hills and hopefully a cattle or two).
Temple (for hapiness when the city grows), a warrior for security/military police (maybe added from another city), maybe a barrack and a few warriors before I can start on the main project for that city: A Wonder (The great library being the no. 1 pri, but I will start building any possible wonder as soon as possible (after the temple).
* Border cities (Cities that are built in the outer part of my land, possbly quite close to enemy cities). Those will get a temple ASAP to widen my borders, then often a worker (to build road back to the other cities/and or improve the terrain). Then barracks followed by military units (and maybe one settler).
* The rest: Will start building warriors if I really need it, but build barracks pretty soon to start getting veteran spearmen and warriors (the latter will upgrade to swordmen later). I also like to get a temple, but that is a lower priority. Those cities will also produce a worker once in a while, and maybe a settler.