Средиземноморский ландшафтный дизайн

Hello Dear Client! 
I was really excited and inspired by the theme of your project. I'm from a country close to the Mediterranean climate so the vegetation is fairly similar here. I took in consideration the ancient aesthetic principles of symmetry, straight lines and proportionate segments, meanwhile connecting to the more natural feel of the surroundings, thus my solution includes a stream with meandering shape (as per your suggestion) and the elevated area around could be more free shaped. the pond-less stream could be procured by company of your choice, I have a suggestion for you to check : https://russellwatergardens.com/pages/pondless-waterfall-kits. They seem to know proper filtering techniques.
Although I gave elevations, please note that there will be mismatches with reality since there is no geodesy file with the actual attitudes. I believe the terrain as is should be suitable for the solution I provide, I tried to represent it in the 3D model. The mass excavated for the water feature could be added for the top elevation where the bushes and flowers group is and creating a sort of alpineum.
I liked the Tuscany pergola idea, I imagine luscious Bougainvillea growing around the beams, creating a shade in the heat. I suggest separating the carbage cans with a wooden screen for easier access, there are many practical and creative solutions on the web, there are options with small pots attached so the cans would be completely out of sight. 
I indicated in the elevation views possible positioning of the ancient art replicas or patterns. 
As for flowers and bushes selection I have a list of suggestions : border flowers: Phlox subbulata, Lobelia, Begonia sempervirens, Assylum, Euonymus japonica; Lavender, Hydrangea (near the bench it is good for shade), Pelargonium in ceramica pots, olive trees, Periwinkle, Hemerocallis, decorative grasses such as Carex and Festuca, Thuja occidentalis ' Smaragd', Cupressus sempervirens 'Tiny tower' ( the evergreens are very common in the traditional Italian and Greek gardens as well as the olives and citruses). There are many species that would be suitable and are not on the list. If you would like me to create a more detailed flower arrangements please feel free to reach out to me so I can make a detail of the garden.
I hope you like my solution or at least you are inspired by some of my ideas. Thank you for your time and attention!