Is your professional not offering any input? Concrete is typically the least expensive material (including prep and installation) with manufactured pavers second and natural stone the most expensive.

Shape is your choice but rectangular/geometric is generally less expensive than a more curved, organic shape.

Thank you! We have a contractor to install the patio but not design and a gardener designing the plant aspect.

Will there be grass? Whatever shape you select for the patio, I prefer ADA compliant pavers, I would curve the planting beds for movement & interest.