Were the bricks an attempt at protecting from predators? It will help, keep animals from burrowing under. But if you took the bricks out of the middle (if this is possible) that would keep the protection, but allow them access to soil.
Sand would help absorb moisture and give them grit. The straw would give them something to do, chickens like rooting through stuff. So personally I would sand the coop (deck sealer is a great idea) and run then straw in the run. this way generally you would just need to sweep out your coop...
You do not have a garden? Do not use potting soil, they put other things in that. I know you can buy dirt, but I have never had to so do not know where. I would go with sand, you can get that at any store. It would give your hens a bit of grit too.
I personally would do dirt under straw (but I have straw) you want to give them something to dig through, maybe get lucky and find a bug in. Sand would be good too. But really whatever you have easily available. Grass clippings in the summer are wonderful for them, wood chips have a nice...
It looks like your floor is wood? Then yes I would put rubber down first. On top of that use what ever is most available to you. I personally use straw, others use wood chips, mulch, ect, what is really important is to use whatever you have or can easily get.