First test is always; do they fit your feet well.
Second is what you're using them for. I like to try and use a shoe specific to the problem, not the rock type. For example a soft last and soft rubber compound might work really well for digging your toes in on a roof problem on grit, but will be next to useless if you need to stand on and put all of your bodyweight through a tiny gritstone pebble!
Really important therefore to have more than one shoe available if you can.
That said, if you only want a single pair then good all rounders that spring to mind for grit are Scarpa Instinct VSRs, Scarpa Chimeras, 5.10 Pinks, 5.10 Anasazis and La Sportiva Solutions.