Use your ears not instruments, unless you have a purpose built room and even then the sound is down to personal preference.
Given that this is a static room, you can create a sound system which only needs your ears to sort out.
Remember subs are not directional at all and high frequencies bounce around all but the best custom designed room. Personally if you are using two subs, then have one behind you and one in front, and balance to taste. Subs are not meant to be heard but zre to create a feeling of a low bass.
A DSP is just a signal processor, and comes in all shapes and sizes with a variety of different functions, from creating a multi point audio out to tailoring the eq for your needs. The quality of this can vary immensely, and can include a the A to D which is usual or just be stand alone.
Given this is only HDMI I am assuming the quality is not going to be that great