Hi lostshopper,
The first suggestion I would have is to read “how to look for and find the best mattress for YOU” which will point you in the direction of some of the most important basic information on the site and give you a step by step process that will greatly increase the odds of ending up with the best possible mattress for your needs and preferences.
A wool/cotton/innerspring mattress is not so common these days and they are mostly made by custom or specialty manufacturers and tend to be quite expensive. Two of the manufacturers of this type of mattress that are closest to you in NJ are listed in post #4 here (one in Jersey city and one in Clark, NJ).
In the other direction … the better choices in the Baltimore area are listed in post #2 here.
There are different types of foam and all of them have a wide range of different qualities and properties. The overviews in the post I linked earlier has more information about them but in general they are polyfoam, memory foam, and latex foam. The advantage of a good quality foam is that it is much more cost effective to make a softer more pressure relieving mattress than using thicker layers of more costly natural fiber materials which also require more specialized or hand building construction techniques. Natural fibers also tend to compress and become firmer over time.
So the first step I would take is to do a little reading to get a more clear sense of the type of mattresses you are likely to be happiest with. This means learning to think of a mattress as a combination of materials used in either the upper comfort layers (which provide mainly pressure relief) and deeper support layers (which provide the support of the mattress to keep you in alignment). The most common support layers would either be an innerspring (there are many different types but all of them perform a similar function as a support component), polyfoam, or latex and the most common comfort layers will be polyfoam, memory foam, and latex (although there are other less common comfort layer options such as microcoils or natural fibers such as you were mentioning).
Once you have read some basic information … you will be in a much better position to ask better questions and recognize the better retailers or factory direct manufacturers that will help you make the best possible choices based on materials rather than marketing information and hype. This basic information should (hopefully) keep you away from the major brands and the mass market outlets that will confuse and frustrate you more than help you find a great mattress.
Phoenix