I must concur with happyturtle. Her proposed site gains a second hill in the BFC, boosting the city's hammer output. The extra food in the lakes from the lighthouse is sure to be vital for the city's growth on to said hill. It loses the silk, but that's calendar - we won't be getting it for a while anyway, so no big loss, and the oasis site also has silk anyways. While it does overlap with the capital's BFC, the overlap is all of a tundra and peak, so it doesn't really matter. I notice that it also loses a lakeside jungled grassland, but that jungle would need to be chopped down before farming or cottaging it. If farmed, it would give 3f, which is the same as the total extra food granted in the lakes when the city builds a lighthouse (one per lake, three lakes = 3f). Otherwise, it would be one cottage. A late starter for the early cottages.
But of course the oasis site comes first.
As for planning, well, settler in 2 in the capital, I suggest a worker afterwards. The city won't grow yet, but with how much food we have, it will grow in three turns - onto unimproved tiles. So we should get that second worker out since we will be having 2 cities in like 6 turns. Then that new worker should mine the forested tundra hill S of the capital. Then we could start on a new settler after getting another pop three turns after the worker is built, have the chop go into that, and the new pop working the mine, should speed it up nicely. Of course, we are lacking for warriors, so we might instead want the chop to go into some of them. What do you guys think?
Oh and for tech I suggest Switch to Mysticism -> Finish Sailing -> Masonry? so that the oasis city can get started on a Monument right away (new city in ~6t, Myst in 4t), and to hook up that marble, maybe even build the Great Wall (in the oasis city) to keep those nasty barbs out.