Hi jennyc2015,
Choosing a mattress for a Murphy Bed would involve the same process and steps as choosing a mattress for any other type of bedframe except you would be a little bit more restricted in terms of the thickness of the mattress and also by the “floppiness” of the mattress materials when your murphy bed is upright. Post #23 here and post #64 here may also be helpful. I would tend to focus on an innerspring mattress (with helicals joining the coils rather than a pocket coil) or a mattress that has a firm and fairly “stiff” polyfoam support core with glued layers.
Other than that … the first place to start your research is the mattress shopping tutorial here which includes all the basic information, steps, and guidelines that you will need to make the best possible choice … and 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” and PPP (Posture and alignment, Pressure relief, and 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).
The first “rule” of mattress shopping is to always remember that you are the only one that can feel what you feel on a mattress and there are too many unknowns, variables, and personal preferences involved that are unique to each person to use a formula or for anyone to be able to predict or make a specific suggestion or recommendation about which mattress or combination of materials and components or which type of mattress would be the best “match” for you in terms of “comfort”, firmness, or PPP or how a mattress will “feel” to you or compare to another mattress based on specs (either yours or a mattress) or “theory at a distance” that can possibly be more accurate than your own careful testing (hopefully using the testing guidelines in step 4 of the tutorial) or your own personal sleeping experience (see mattress firmness/comfort levels in post #2 here).
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There are also no “standard” definitions or consensus of opinions for firmness ratings and different manufacturers can rate their mattresses very differently than others so a mattress that one manufacturer rates as being a specific firmness could be rated very differently by another manufacturer. Different people can also have very different perceptions of firmness and softness compared to others as well and a mattress that feels firm for one person can feel like “medium” for someone else or even “soft” for someone else (or vice versa) depending on their body type, sleeping style, physiology, their frame of reference based on what they are used to, and their individual sensitivity and perceptions. There are also different types of firmness and softness that different people may be sensitive to that can affect how they “rate” a mattress as well (see post #15 here) so different people can also have very different opinions on how two mattresses compare in terms of firmness and some people may rate one mattress as being firmer than another and someone else may rate them the other way around. This is all relative and very subjective and is as much an art as a science.
In other words the only way to know for certain whether a mattress will feel “plush firm to plush” for you (regardless of whether it feels “plush firm to plush” for someone else) will be based on your own careful testing or sleeping experience
There is also a lot more information in post #2 here and the more detailed posts and information it links to about safe, natural, organic, “chemical free”, and “green” mattresses and mattress materials that can help you sort through some of the marketing information and terminology that you will encounter in the industry and can help you differentiate between them and answer “how safe is safe enough for me” and that can help you decide on the type of materials and components you are most comfortable having in your mattress or on the certifications for harmful substances and VOC’s that may be important to you. These types of issues are complex and are generally specific to each person and their individual sensitivities, circumstances, criteria, beliefs, and lifestyle choices. Mattress materials that are most commonly used in the industry that have a reliable safety certification for harmful substances or VOC’s certainly wouldn’t be “toxic” based on most people’s criteria.
If you are looking at online options then the tutorial also includes several links to lists of the better online options I’m aware of (in the optional online step) that include many different types and categories of mattresses in a wide range of budgets and firmness levels that would be well worth considering.
If you let me know your city or zip code I’d also be happy to let you know about the better options or possibilities I’m aware of in your area as well.
Phoenix