Help Building an Audio Room

That's probably overkill but maybe you can find a few ideas to incorporate in your new space.

I highly advise not having a square room because of the room nodes you will build into the room automatically by those dimensions.

Do some reading if you have the time on acoustics with room nodes.

15x12 is better than square. Maybe you can go 15x20? The more you can stay away from square the better off you'll be - at least acoustically. You'll still need some bass traps - especially with poured concrete walls.

B

Pick up a copy of Robert Harley’s Complete Guide to High End Audio. There you will learn why it is so desirable that room dimensions not be multiples of each other. He even shows how to calculate and map room modes. 
Slap echo is a function of unbroken flat parallel walls with little to nothing to do with concrete. You can frame sheet rock over all of it and have the same slap echo. This is handled with diffuser and/or absorption panels. 
The smart move is to build one wall to reduce one dimension to 12 or 13 ft, and use the space behind this wall as a large hidden bass trap. The wall can incorporate storage shelves so it isn’t even wasted space. This wall might even be angled. Mike Lavigne incorporated this exact technique in his exceptionally good acoustic response listening room. 
 

Whatever you do don’t freak out and overreact. My room when it was bare walls and floor was hideous. Merely adding furniture and components is a huge improvement. 
 

The good news is the greatest gains are made from the first small steps. Do those few things, get your system in place and listen. There is no substitute and there is no doing it right the first time. Mike paid big pro’s big money and then still came up with even better sound simply by listening and experimenting. 

Thank you both for the level-headed input.  
I love the idea of a bookshelf/built-in wall to effectively build one wall out and provide some trap and diffusion in doing so. I think that will go a long way, and I can see in the pic they did something similar. 
If I did that on a side wall, I might explore building the front or back wall with a bit of angle; top edge of wall built out 6-10” more into the room than the bottom or vice versa. I’m thinking that may help and be barely noticeable. 
The cost is essentially the same to the builders/me, but as I socialized the idea with them a few weeks ago, they said, “That’s a first. Build it out of square?.. We can do that.” 
I’ll check out the book, too. 
Thank you again.