Hi zmberch,
Welcome to the Mattress Forum! 
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 know 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 (Posture and alignment, Pressure relief, and your own Personal preferences) 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).
Outside of PPP (which is the most important part of “value”), the next most important part of the value of a mattress purchase is durability which is all about how long you will sleep well on a mattress. This is the part of your research that you can’t see or “feel” and assessing the durability and useful life of a mattress depends on knowing the specifics of its construction and the type and quality of the materials inside it regardless of the name of the manufacturer on the label or how a mattress feels in a showroom or when it is relatively new so I would always make sure that you find out the information listed here so you can compare the quality of the materials and components to the durability guidelines here to make sure there are no lower quality materials or weak links in a mattress that would be a cause for concern relative to the durability and useful life of a mattress before making any purchase.
I’m sorry to hear about that. 
There is no one firmness level or style of mattress that is “best for backs” in general because it would depend on the body type, sleeping style, and individual preferences of the person. While the most common cause of lower back pain is a mattress that is too soft … it can also be caused by a mattress that is too firm and doesn’t provide enough “surface support”.
Each person has unique needs and preferences in a mattress so a mattress that would be a “perfect” choice for one person in terms of comfort, firmness, and PPP may be completely unsuitable for someone else to sleep on that has a different body type, sleeping style, or preferences and sensitivities. The only “first-hand experience” that matters is yours when you try out a product for yourself.
A mattress certainly needs to have deeper layers that are “firm enough” to stop the heavier parts of your body from sinking down too far and make sure you sleep with your spine and joints in good alignment and upper layers that are thick and soft enough to “allow” any pressure points such as the hips and shoulders to sink down far enough to relieve pressure points in all your sleeping positions as well but “firm enough” and “soft enough” can vary widely from person to person. If you’re interested, there is more about primary or “deep” support and secondary or “surface” support and their relationship to firmness and pressure relief and the “roles” of different layers in a mattress in post #2 here and in post #4 here that may also be helpful in clarifying the difference between “support” and “pressure relief” and “feel”.
These posts are the “tools” that can help with the analysis, detective work, or trial and error that may be necessary to help you learn your body’s language and “translate” what your body is trying to tell you so you can identify the types of changes that have the best chance of reducing or eliminating any “symptoms” you are experiencing (at least to the degree that any symptoms are from your mattress rather than the result of any other circumstances or pre-existing issues you may have that aren’t connected to a mattress).
While it’s not possible to “diagnose” mattress comfort issues on a forum with any certainty because they can be very complex and there are too many unique unknowns, variables, and complexities involved that can affect how each person sleeps on a mattress in terms of “comfort”, firmness, and PPP or any “symptoms” they experience … there is more about the most common back pain symptoms that people may experience when they sleep on a mattress and the most likely (although not the only) reasons for them in post #2 here .
In general … what you would be looking for is a mattress with firm enough deep support and then comfort layers that are “just enough” in terms of thickness and softness to “fill in” and support the more recessed parts of your sleeping profile and relieve pressure in your most pressure prone sleeping position (usually side sleeping for those who sleep in this position) so that there is less risk to alignment in your other sleeping positions.
For those that have a more restricted budget then post #4 here and the posts it links to also include many of the better lower budget online options I’m aware of as well.
Phoenix