For the glory of the King, I have taken the time to play and meticulously document the first 35 turns for both the Agriculture/Farm start and the Meditation/Mine start. My hope is to give the King all the available information on which he can base his good decision. If his Highness sees merit in both this and the Fishing first plan I will run that plan through the same process.
The Excel Spreadsheet which gives all of the meticulous details of every single turn is here:
Plan Comparison v1.0
It should be somewhat self explanatory after some examination. Feel free to download the Alternative reality start save file I provided above and play through it all yourself.
To summarize:
Agriculture/Farm First - classic opening
By turn 38 we have the following techs researched: Agriculture, Bronze Working, Hunting, The Wheel, Meditiation (for comparison - could be anything).
We have produced: A worker, A warrior, a barracks, A warrior, and begun a settler (at our current city happiness population capacity of 5).
We hit our city growth cap on turn 30 and had to stagnate our growth to avoid angry citizens at that point.
Meditation/Mine First - Religous opening
We found Buddhism, increasing our immediate Maximum population cap to 6 (8 with the mine and a temple, and other religous benefits).
We have the same techs as above but we manage them by turn 36.
We have produced the same units/buildings, although we are 1 turn behind by turn 33. Although we lead in production through most of the opening game on turn 26 the Agri/Farm ties it up and on turn 31 they pull a point ahead (the higher population catching up).
On turn 33 That Farm/Agri strategy is 1 population point ahead, however, they have reached their cap of 5 (6 when the road to the gems is complete) which will take longer to construct. We can grow unrestricted to size 6 (7 when the road is complete) because of religion - and even higher - to size 8 - with a temple.
The biggest question is whether we stagnate our growth at 4 to build a Settler, or wait 4 turns to grow to size 5 (the cap that the Agriculture/Farm start strategy is at) before we build the Settler and then continue on with our growth as we don't have the same size cap.
Extrapolation
Yes - quickly gaining population is important. And the Agriculture/Farm strategy does pull ahead early with this. But it's sort of like a jump start to know where - the Meditation/Mine strategy gets the same food resources hooked up a few turns later, but with a growth cap of +2 (with a temple) in the cities we can grow to 8 instead of 6. This gives us a massive advantage across the board until we discover Hereditary Rule.
All that said, I'm just giving my point and ideas. I will completely support the King and his initiatives