One step of your beginning would be to request acoustics plans or your room from GIK and/or ASC. They will usually do that for a small fee, applicable to future purchases. The plans will give you ideas and openings to ask questions. If you ask both firms, you'll get an idea about how much ideas vary on best approaches. (Both are highly reputable.)
I would also browse the acoustics fabrics collection of Guilford of Maine. Many cloth-covered acoustic panels can be made with any GoM fabric, and there are many, some of which are gorgeous.
You might consider buying a measurement mic (miniDSP UMIK-1 or UMIK-2 is cost-effective and widely supported) and downloading REW measurement software. That will allow you to get an idea of how your room is working now, and also how that changes as you add acoustic treatments.
Then start reading. I can’t list resources -- I did it by looking around -- but I’ll bet others will have good ideas.
There is a lot about practical acoustics on the Web. (I do not recommend the books by Robert Harley.)

