Most cost-effective Sound proofing

There's a difference between sound proofing a room, and sound tuning a room.

Sound proofing is isolating the space from noise pollution occurring outside the room, as well as preventing what you are doing inside the room from leaking out.

It's going to be pretty tough to do in a "standard" bedroom. Your biggest problem will likely be the transmission of low end frequencies, because there are just too many of these transmission paths between rooms in a house.

I need some advice with methods to make my room sonically optimal for recording

As far as sonically tuning a room to better your acoustics, well, in a space like that, there's only so much you can do. That's not to say that you can't improve the space, but as far as making it "sonically optimum"?
Probably not gonna happen. You can always improve... but in a limited space like that, only so much.

And even if you could cover your walls with 1" foam, ( which I don't recommend, by the way), it won't do a thing for frequencies below 1 k.

The area rug will do a little, it may attenuate some flutter echo up in the top end, but probably not much else.

Without seeing/hearing your room, or knowing the dimensions, it's pretty tough to make any recommendations. You may want to consider fabricating some do it yourself bass traps for the corners... plenty of info on DIY projects all over the internet that involve nothing more than some 1x2's, some insulation and some pegboard... but if you're hoping that you will hear incredible results in a room that size and of that construction, well, you may hear some improvement, but I doubt it will be drastic, and I'm not even sure it will even be noticeable enough to warrant spending money on it, if money is that tight right now.

The best thing you can do right now is to try and make your area better acoustically for mixing purposes, not for recording purposes. If you are going to spend any money right now, you should look at good reference monitors... BUT... even the best monitors you can buy will only make so much of a difference if your room is "lying" to you.

My recommendation? And I could get shot down here from my colleagues on this... while I don't normally recommend it, you should probably look at mixing with headphones... and through a process of "learning" the phones - this is where you would do a variety of mixes and then play those mixes back on other systems (car audio, MP3 player, boom box, etc) and get a feel for where your room is hot or shy in terms of the frequency response of your headphones. You can "learn" what your headphones are doing in relation to how your mixes sound when played back on other systems, and you can grow accustomed to what you need to do in relation to those differences.

In my humble opinion, of course.

"The area rug will do a little, it may attenuate some flutter echo up in the top end, but probably not much else."

A rug is always recommended under an open mic when a hard surface is present beneath it to reduce early reflections.

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Unfortunately, you are going to find the information discouraging. As DonnyThompson indicated, you can't make a small room sound great. You can do some inexpensive things that will make it sound better. You can build bass traps. You can put a cloud above your mixing area to cut down early reflections.

I am not going to shoot down the idea of mixing with headphones. It may be the best solution, and it will almost certainly be a part of your workflow. The better you can make your room, the smaller a role for the headphones.

In regard to your comment about insulation, you are probably thinking about the wrong type of insulation. The material you would use to build bass traps is Owens Corning 703 rigid fiberglass insulation or something similar. Be very careful about "something similar." Your intuition is right. There is a lot (heat) insulation that is NOT effective at absorbing sound. Make sure you get something that has been tested for sound absorption. Do a search on "super chunk" bass traps. As you wander through the web checking out those links you will find other DIY projects. Check out your local prices for building material. This will give you some idea of the general budget required for these projects. If some of them seem feasible, post in the Studio Construction and Acoustics forum with a detailed description of your room, your building constraints, and your budget.