Aluminum Mesh Screen Fabric - Installation Question

A big question - like how to do it.
No spline system like big box stores sell - don't like the vinyl cover pieces that snap over. Altho it all looks really easy to install. Our porch needs painting and so we will need to replace screening. (aluminum mesh material)
Original porch had the fabric stretched around and then the mesh staples in place every few inches. Stapled seams covered covered with cedar (same wood as rest of porch).

It is all painted and now time to screen. Hubby got fibermesh, it is very soft unlike aluminum and hard to stretch drum tight to staple. Also, I'm reading won't last as long as the aluminum and impossible to repair if needed. So will get the aluminum and take back the unopened rolls of the fabric but wondering -- when installing -- is it best to staple along the top rail of the opening being covered then pull tight and staple along the bottom rail (horizontals) and then do the sides ( verticals)? Or, is it better to staple up along one side, pull tight across the opening and then staple the other vertical .... After the two upright sidws fasten along the top rail and finally the bottom? I would say the largest opening ( length) is is about 12 foot wide and maybe 5 feet high. I figure not good to pull on the diagonal. THANKS ahead of time. Don't want to crease or wreck the aluminum mesh-- as it is I have to go to war to get him to return what we have but I don't want to be doing this again in 4 years. The aluminum is in great shape after 12 years --- just could paint the slats because the builder put the screening in front of what needed to be painted. ;o(