Hi there !
I would build the core of the oven( firebox) out of 2 inch firebrick. Use refractory cement or masonry cement. The firebrick can be laid up on its edge( not flat) as it is expensive and still will stand without support as your lay it up. Regular brick (solid not perforated) can be built around the firebox in any shape you want. Usually one doesn't cement the outer brick to the firebrick core. A space is left between( half inch to inch) which is filled with dry sand as you work your way up. This allows for expansion .
It is tempting to save money and buy the thin firebrick but it cannot be used free standing so you need to cement it to a common brick wall which doesn t allow the space with sand , which will allow the oven to last much longer , as it is the constant expansion and contraction that will eventually cause the oven to crumble.
Firebrick can be bought in yellow or brown. the brown ones tend to be harder and more expensive.
As far as insulation goes we always use mineral wool if you are insulating against combustible material? not quite sure of the purpose of the insulation. There is no need for insulation around an oven unless there is danger of overheating surrounding combustible material. You can build as much brick and stone around the firebrick core as you like. Make sure the base of the whole thing is good and solid.
In general when using a baker/pizza oven the core is heated quickly using
kindling type
wood, not big slow burning wood. Then it is cleaned out and the baking is done. A piece of insulation can be used as a door to close it during baking. Others brick up the door or have a stone that fits. Traditional baker ovens usually had a
cast iron door with a peek hole.