I've been using Owens Corning #703 and #705 rigid fiberglass panels for years. They're easy to hang on the wall, and you can make freestanding panels out of them, with an inexpensive wood frame, allowing you to move them whenever you like. I make these and use them as first reflection point absorbers when someone has a room with a wall on one side and an open wall on the other - nearly impossible to get good imaging in a system like that without those panels. You can cut bevel edge profiles on them, and once wrapped in acoustic fabric they look just like factory. BTW, for health reasons, you will want to cover them with acoustic fabric!!! But...
If you want to do this right, the first thing to do is figure out what frequencies you need to absorb, if any. The only way to do this properly is by measuring the system with a meter that displays some accurate version of an RTA or an FFT. You play a verified accurate pink noise signal through your system (as close to a reference signal as is practical) and you measure the frequency response at the listening position. The variation from a flat response curve will tell you what your electronics, speakers and room are doing to the reference signal. Armed with these facts you can make an informed choice.
If you want your system to sing, this is not a great time to slap whatever you can get your hands on onto the wall and see if it sounds "better". Egg crates, packing blankets, shag carpeting, etc. aren't acoustic treatments, though they will change the sound. These fiberglass panels are inexpensive, reliably consistent, and easy to work with.
If your speakers and electronics are above average, they shouldn't
mangle things too much. Usually the worst component issues are speakers that are either too bright or not bright enough in the high frequencies. And bass problems, caused by either the room or the speakers, are a discussion for another day. But your room is almost guaranteed to be making a
mess of things in one way or another.
Once you know what frequencies you want to absorb, you want to look at the absorption characteristics of the various acoustic materials to find one that grabs those frequencies and little else. This can be hard to do, but it's always worth the effort! All things being equal, thicker absorbers will help with lower frequencies. If you just need to take the harshness off from 8kHz and up, you might be fine with a 1.5" thick absorber. If you need absorption from 2kHz-8kHz, you'll need a bit thicker treatment. The Owens Corning website gives acoustic absorption figures for their various density panels, so you can make a good choice.
Too much absorption and the room becomes acoustically "dead". Too little and you may have slap echo, comb filtering, excessive decay times, etc. that make your system sound jumbled and chaotic. It's possible that you don't need to absorb anything...that diffusion is what you need. Diffusion preserves the energy in the room, but scatters that energy, minimizing effects like slap echo and comb filtering without deadening the room. Only proper measurements can tell you if this is the case. I've measured hundreds of rooms, and a light touch has always been the key to proper absorption.
Also, don't neglect your listening chair; if it's back is at or above your ear level, is likely mucking things up, and absorbing lots of high and upper midrange frequencies. I swapped out a comfortable recliner for an IKEA low-back chair, and the improvement was dramatic. I never went back!
If absorption is required, the typical major offenders are the first reflection points at the front wall between the speakers, and at the side walls. The oldest trick in the room treatment book is to have a friend slide a mirror along those walls, tight to the wall. As soon as you can see the tweeters centered on the mirror while you're sitting in your listening position, that's likely where the treatment will be most effective. Also, centered behind the listening position is often a prime location. If done correctly, you'll find that the imaging becomes much more defined, even holographic, and it becomes much less fatiguing to listen to your system (i.e. you have to be physically torn away from listening). Because there's less chaos in a properly treated system, you'll find that you hear more into your music, even discovering things that you had never noticed in music you've heard a thousand times.
Final tweaking should always be done by critical listening, but evaluation, location and material choices should always be done by measuring. In my experience. Hope that helps!