The point of bracing is to reduce vibrational sound radiated into the air. So bracing along the box internal edges, as I did back when I was a teen starting my journey to become a loudspeaker engineer, is not too helpful ha ha. You want to brace front-to-back, top-to-bottom, side-to side but ideally NOT to the center of the panels. You want off-center so the remaining "free to vibrate" portions are each different sizes which will resonate at different frequencies.
I like to use 1x1" dowel, and have them all meet in the middle. I cut the dowels very slightly too long, then twist fit in place, then glue on on side. Dry like a day, rotate, glue the next side, repeat repeat. Also some kind of anti-vibration coating would be good, and also stuffing. For stuffing get Vance Dickason's seminal Loudspeaker Cookbook which at least in the 7th edition has a chapter about that. Even more extreme you can make the walls a sandwich of wood-stuff-wood where sorry I forget what the absorbent stuff in the middle is.
Are you doing sealed or ported? Ports are a whole 'nother thing.
And you are making two subs, to put in different locations? You have room correction that can adjust two independently?
To calculate the box size, you need the Thiele-Small parameters for the driver. There are several 10" Purifi it seems, so you would have to decide which you will use and by the way you know they are like $800+ apiece?