Now that you're down to bare structure your options are endless.. and good on you for not replacing with carpet!
I think vertical boards will look better.. they can be glued in place easily enough. Another option that will leave the interior brighter is the 'herreschoff' look, white laminate with stained wood trim around the edges. Veneer or plywood panels can also be glued but requires more careful cutting and fitting to avoid unsightly gaps. Some tidy trim moldings around raw edges will leave a better look.