One of the reasons the carpet is not a good material for the studio is that it is messing with the reflections bouncing off of the floor which is a vital component of how we perceive sound in our natural environments. The same, of course, goes for excessive use of absorbing materials in walls/ceilings, etc. It's really hard to re-adjust yourself to a new hearing environment every time you walk into your studio and start mixing.
Curtains, almost never, will do the job correctly, they need to be insanely heavy to work, or packed 5-6-7 together to create something that works. Absorbing panels on the other hand are great.. you want more? you make more! but curtains? you do what, you stack them? how many rails? what if you want them a bit left or right...
The control room must be have balanced sound, some reflections are ok, some Reverberation Time (RT) till some point is ok too, what's not ok are peaks and dips (amplifications and cancelations) in the frequency spectrum. Phase problems in stereo imaging are also not ok and the list of course goes on.
Studios used to be super packed because they had to fight problems on a very large scale, like mains monitors ranging down to 5Hz, live rooms and/or guitar amp rooms with very loud DBs and stuff like that.. nowadays most people just mix in their rooms with small monitors so the scale of the problem is substantially smaller.
One of the most important things that must be done correctly when designing a control room is the placement of the speakers and the monitoring volume you like to mix at. This is what is going to be dictating what must happen to a room. If on the other hand you just walked into your room and said, that's where the speakers go, you might be in a lot of trouble.
Sound, especially in the lower frequencies is not something easy to handle, you'd need massive amounts of weight to stop certain frequencies in the lower spectrum, so more or less, in a project studio environment, these frequencies are considered as untreatable (treating them has people going to extremes by using 1-2-3 subwoofers to balance out some dips and other crazy techniques) but moving a speaker 1 meter forwards or backward can work wonderfully.
Because the problem of treating a room is a rather broad and complex one, I will assume that you have chosen the best possible position for your speakers in the room by doing some kind of measurement.
Now the curtains you are referring to have to do with absorption, one of them also supports that:
Up to 1.0 NRC Rating lab tested. This means that 100% of the sound is being absorbed by the curtain!
That's just plain misdirection and misinformation, what's the frequency(ies) of the sound? what's the volume? 100% absorption? is this curtain sucking all the air from the control room? sorry, but I will just ignore it.
Your best bet is constructing some wooden frames and fitting absorbent materials like Rockwool or Fiberglass 50kg - 150kg depending on how rigid you want them to be (rigidity is inversely proportionate to the frequencies you are aiming at treating) and placing them at the first reflection points to start clearing the image and start having a more natural soundstage.
The mathematical equations to do that are in the following picture commonly found around the internet (I think it belongs to realtraps.com):
(The rigidity of the material is mentioned because a very rigid material can still reflect very high frequencies, as a rule of thumb 50-75 is a bit more broadband)
After treating the first reflection points, you could add a thin carpet if, for instance, you have a marble or cement floor that doesn't have the best sound properties. If you have wood, leaving it as-is is a very good choice or again a thin carpet could help so definitely test it (the carpet should be relatively small covering 2-4 sq meters in total..)
If you have a window as you mentioned, I would make some kind of internal cover which I could open when I'm not mixing and I don't care about reflections.
Now, this, of course, is only the start, generally, if everything is executed and done correctly, a little goes a long way with absorption, you'd want to cover a percentage of your room and then stop. Also, it's a good practice when not treating a reflection specifically but just adding more absorption for the RT, to leave good surfaces uncovered (wood - mostly).
Of course, there are countless other topics like diffusion and resonant traps and slat resonators and the list goes on, but in my opinion, this is a good starting point for anyone who wants to have a better mixing environment.
If all these seem insanely difficult to you, mix with headphones :)
If you are recording with a condenser microphone, then this is even more relevant to your problem. Generally dampening the Reverberation Time of the room makes recordings and mixing better.
A condenser mic will pickup a bad recoding room, a Dynamic mic will not (that much) A condenser mic will sound godly in a great room, a dynamic will sound roughly the same in both cases.
Also, this forum: John Sayers' Recording Studio Design Forum is gold, of course, GearSlutz and other well-known forums are great as well.