I have been at this in my room for 7 months. I started off just trying things here and there and listening. The number of places to put things seemed infinite. I had blankets and towels everywhere, bought some panels, moved them around. It was time consuming and crazy making. Then I took some advice I had been resisting -- buy a $100 mic and download REW, Room EQ Wizard. Learn the basics. Measure, treat, listen. Repeat. Learn where your room’s reflection points, peaks, and nulls are -- for real. In some cases, theoretical predictions were correct, in other cases, they were way off -- because I have an odd room.
I bought OC 703 panels and wrapped them in fabric. With 6 of them I made two 2" panels and 2 4" panels (doubled up in side a fabric pillowcase). These proved to be very effective tools to test out various effects in the room, especially when doubling them up and leaving space between them and a wall. They were excellent preliminaries -- in conjunction with REW and listening -- and gave me confidence about how much treatment to invest in later. Throwing money at the room acoustic problem is more wasteful than throwing it at gear because it's much harder to recoup by selling. And it's hard to integrate into an existing domestic arrangement.
Set some goals, get the right tools, work patiently and incrementally. My two cents.