Wood fired oven can be dome or barrel as you desire. However, the dome oven stand out the most efficient for wood fired oven because it is able to distribute heat even in the oven to ensure uniform cooking of your pizza.
The standard and mainstream wood-fired pizza is costly to build, but by sourcing the materials required locally, you can cut down the costs tremendously. Fire bricks are the mainstream building materials used, but you can also bake adobe bricks locally and they will serve the same purpose. Alternative, if some bricks remained when you where building your main house, they can too be used to build the wood-fired oven.
With the required materials, then set up the oven foundation and follow the standard building procedure.