I have tried a few different ways, and I like going Wheel->Pottery as this times very well with the worker finishing the mine & pig road. He can then immediately build 2 cottages (which we will not use immediately of course). Our big advantage is food, we do not need as many farms to grow so we can work more cottages. After 2 cottages the worker roads to city, with extra cover from expanded borders and a fogbusting warrior.
After that, Archery might be best simply so we are ready to build an Archer the turn we finish the Settler. (we will need to send a warrior to where we want to settle to fogbust and make sure the settler and worker survive). Building an Archer now is sensible as soon the Warriors won't count to the MP's we need in the Cap to found new cities.
Then.... its the big question. Do we research BW before settling city 3?
Pro's : we get Copper

and we can chop and mine like crazy, we need only 2 more Acrhers/Warriors and a building (Granary) to found city 3
Con's : no founding city 3 until we have 6 archers/axes/spears and another building
We can of course chop out a lot of units, but they will start costing us in maintenance. 6 Archers & 4 Warriors cost 2 gpt in unit maintenance, even with 3 cities built.
Here is a thought bubble about where we could settle. The red or yellow tiles with the units on them. The other red & yellow dots are just me trying to see how another city would fit with them
Both dots share the pigs, which the capital could borrow back when it needs to grow so we can settle a new city. All cities are on the rivers, as the health bonus looks like it will be important (we can not see many bonuses)