Room treatments and acoustics…. How to begin?

I second GIK. Great website, nice designs, effective acoustic panels.

I would begin by experimenting. Use couch cushions, pillows and blankets. Put in your room descriptions into and AI and ask for some likely placement of treatments. Then use stuff around your house to try it. Listen. This will give you some idea of the sonic benefits you will get and how to tune. 

Then as an AI on what you should read to create and build traps... if that is what you want to spend you time doing. Or engage and buy from ACS. Or you can use stuff like I have... heavy wool oriental carpets as wall hangings and pillows... etc. if that blends with your decor better. 

I have taken pictures of my listening space and downloaded them to ChatGPT which is incredibly easy and allowed ChatGPT to provide ideas and advice and it works pretty well.

use iphone audio function generator app (f Generator) to sweep audible frequencies to hear if any resonances in your room.. then fix findings, in furniture pictures on the walls etc.. next step is a more precise measurements of reflections, adding sound absorbing panels etc..

I caution about employing typical commercially available bass traps with the expectation that they will help much below 100 Hz. To better mitigate deep bass modes, incorporating multiple subwoofers (at least two and up to four) will do a better job. You could also consider PSI Audio AVAA devices. 

For the higher frequencies, you will want to address first reflections on the ceiling, floor, and side walls. Opinions are mixed about diffusion and absorption but I endorse absorption.

These two approaches will likely give you the best and biggest bang for the buck but further acoustic treatment is likely to clean up the sound even more.  But at least, start here.