How would you prioirtize?

You got a lot of good suggestions. A quick and easy and inexpensive thing that will help improve sound quality is to get rid of those blue jeans speaker cables.  I am not a proponent of expensive cables, and BJC makes some decent cables, but when I tried their speaker cables they seemed to suck some of the life from the music. 

Do Try various Sub Plinths and Footers arrangements under the TT.
Energy is transferred to a TT through Air and Structures.

The Sub Plinths and Footers will attenuate the environmental effects.

I have not at any time found this practice to be a wasted investigation.
The outcome has been to discover a comprehensible perception of a  improvement to the presentation.

My Investigations, 'that are limited' for working with a Cabinet Speaker Set Up, are that Sub Plinths Produce noticeable improvements.
 
The Perception of a sharpening of the Imaging and producing a Leaner Bass Note with a improved Mid - High Projection can be attained,
this is at the cost of a Broad Soundstage.

Seating Suspension Footers between the Sub Plinth and Speaker
( I use Two Tiers of Sub Plinth each with Spiked Footers, with a Set of Three  AT-616 seated on the Top Tier ) has in my experience added a improvement.
The addition of Suspension Footers Widens the imaging and separation, 
broadens the Soundstage in all dimensions, and there is a perception tht the performance has a increased presence, but not as a added weight or richness.  
Note: I feel sure that there will be a group of listeners who would be very satisfied with the Speakers Performance, when seated on the Two Tier 
Sub Plinth before the Suspension Footers were added.

Creating a Two Tier Plinth is Relatively Cheap and worth the time taken to investigate the effect it can have on attenuation within a environment.  

Before an amateur will buy random acoustic panels he must order acoustic analysis of his room. Some rooms are simply awful for sound, some are good. Mos of the cheap acoustic panels are useless.

Instead of GIK you can order room analysis from Vicoustic (I paid 50 EUR for complete 3D model of my room with acoustic treatment).

If you want to learn more (how difficult it can be) you have to watch his lectures online (very informative).

Then you will realize how much you have to pay for a proper acoustic treatment if you will ignore all cheap foam panels flooded the market (or some junk from the manufacturers who promises you a great result if you place a few square little something behind your speakers etc).

Real acoustic panels are made of natural wood, they are big and heavy, this is what professionals have in the studios (like this diffuser).

Absorbers are easier to make, last year I discovered Basotect (remember BASF ? ), they can make any custom size and color, look on their site for pictures.

P.S. I bought these absorbers from Vicoustic two years ago, sadly this model is discontinued. Took this image two days ago thinking how I’m gonna glue them. Those type can be nice in any interior design, I have only two colors. The Wavewood are on my wall behind the speakers for a long time, they are nice. For the ceiling I got Multifuser DC2.

Actually you need panels everywhere (all walls and ceiling), so it can be ugly and expensive!

Here is my old thread about it (hope it will help a bit, maybe).

this is at the cost of a Broad Soundstage.

The cost is too high. Especially considering you can have it all.

@chakster , you want to use ceramic tile adhesive for those, use a base trowel to apply the glue and stay 1/2" away from the edges. You will be able to adjust them a little once they are on the wall and the adhesive has enough body so they will not move or fall off whole they are drying. Otherwise excellent advice. You have to know what you are dealing with before you deal with it!