Saucony Grid Stabil is one of my favorite shoes and I recommend it at least once a day for the narrow (rectangular) foot. Surprisingly it works for shallow (flat) and deep (high arched) feet, because it comes in both medium and wide widths. For a refresher on foot width determination, refer to my blog posting https://drshoe.wordpress.com/2008/01/14/narrow-vs-wide-feet/.
As for the construction, this is one of the few running shoes which is proportional, meaning the heel to ball and heel to toe measurements are true to size (https://drshoe.wordpress.com/2007/12/05/size-matters-heel-to-ball-vs-heel-to-toe/). It’s also deep enough to accommodate a sport orthotic once you remove the sock liner.
It has a non-collapsible heel counter which helps guide heel strike and it has a firm inside mid-sole (grey above) which helps with pronation or foot collapse. Lastly the toe box is shallow meaning it will pass the pinch test (https://drshoe.wordpress.com/2008/01/15/pinch-test-shoe-toebox/), providing a secure fit, if your foot is lower volume than most.