I presume by "gesso" you mean an acrylic primer. I do not prefer this material for preparing a painting ground, but that's personal. "Real" gesso, the stuff the old masters used is entirely different - a compound of hide glue, gypsum and whiting. It is too brittle to use as a painting ground on stretched canvas, but is excellent on panels.
One coat is adequate to isolate the canvas from oil absorption. There is some thought that acrylic co-polymers (which remain indefinitely flexible) have no place under oil paint for archival reasons.
Fine portrait weaves are intended to provide painting surfaces with little or no texture. If you desire the texture of visible canvas weave behind your work, by all means, opt for a coarser weave, heavier canvas.
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