Hi Robicali.
Welcome to our Mattress Forum! 
I agree that it is a good idea to steer away from “name brands” where you can’t find the specifics of the materials within a mattress. While typically, someone’s experience can’t be used as a reliable indicator of suitability for your own needs and preferences I hope that Melisa sees your post and can add a few comments about what she ended up purchasing and her experience so far. I’m not sure what you’ve read since you found the site but just in case you haven’t read it yet … the first place to start your research is the mattress shopping tutorial here which includes all the basic information, steps, and guidelines that can help you make the best possible choice … and perhaps more importantly, as you already stated… how and why to avoid the worst ones.
Two of the most important links in the tutorial that I would especially make sure you’ve read are post #2 here which has more about the different ways to choose a suitable mattress (either locally or online) that is the best “match” for you in terms of “comfort”, firmness, and PPP that can help you assess and minimize the risks of making a choice that doesn’t turn out as well as you hoped for and post #13 here which has more about the most important parts of the “value” of a mattress purchase which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists based on all the parts of your personal value equation that are most important to you (including the price of course and the options you have available after a purchase if your choice doesn’t turn out as well as you hoped for).
The key will be when sleeping upon your side to make sure that you are not sinking in too deeply with an excessive lateral curvature. This article speaks to this in a bit more detail. I am not very sure if “larger framed” also means higher BMI but here are a number of forum posts and threads about mattresses and higher weights and a forum search on heavy (you can just click this) will bring up many of them. Some examples include post #2 here and post #2 here and this thread and Post #3 here has more information and suggestions about heavier weights.
You can always do a forum search just click here and put a key term in to see if what stores have been discussed in Tennessee see the ones listed in post #7 here) that you may be interested to visit.
I hope this gives you a good start with your research for a new mattress.
Phoenix