Hi AnnB,
In general terms most foam mattresses (memory foam, latex foam, polyfoam) and most pocket coil mattresses that aren’t more than about 12" thick will be flexible enough to work well on an adjustable bed regardless of whether they are purchased online or locally or how they are shipped or delivered. When you are over about 12" thick then the mattress may not contour to the adjustable bed as effectively. While in general terms thinner mattresses will tend to be more flexible than thicker mattresses and will contour to the adjustable bed more effectively … this can also depend on the specifics of the mattress layers and components. 12" thickness is only a general guideline because some mattresses that are a little more than that which use more flexible materials may still be fine and some mattresses that are less than that may be less flexible and not work as well but 12" is a good general guideline. The most reliable source of information about whether any specific mattress would be a suitable choice for an adjustable bed will be a knowledgeable and experienced retailer or the manufacturer that makes the mattress.
There are hundreds (if not thousands) of mattresses that are available online but assuming that the materials in a mattress you are considering are durable enough for your body type and meet the quality/durability guidelines here relative to your weight range … the choice between different types and combinations of materials and components or different types of mattresses are more of a preference and a budget choice than a “better/worse” choice (see this article). The most reliable way to know which types of materials or mattresses you tend to prefer in more general terms would be based on your own local testing or your own personal experience. when you sleep on it.
When you can’t test a mattress in person then the most reliable source of guidance is always a more detailed phone conversation with a knowledgeable and experienced retailer or manufacturer that has your best interests at heart (and who won’t just sell you anything they can convince you to buy) and who can help “talk you through” the specifics of their mattresses and the properties and “feel” of the materials they are using (fast or slow response, resilience, firmness etc) and the options they have available that may be the best “match” for you based on the information you provide them, any local testing you have done or mattresses you have slept on and liked or other mattresses you are considering that they are familiar with, and the “averages” of other customers that are similar to you. They will know more about “matching” their specific mattress designs and firmness levels to different body types, sleeping positions, and preferences (or to other mattresses that they are familiar with) than anyone else.
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 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 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.
If you are considering online options then the mattress shopping tutorial includes several links to lists of many of the better online options I’m aware of (in the optional online step) that include many different types and categories of mattresses that use different materials and components in a wide range of designs, budgets, firmness levels, and with different return/exchange policies that would be well worth considering.
If you are also open to local choices that you can test and compare with each other in person then if you let me know your city or zip code I’d be happy to let you know about the better options or possibilities I’m aware of in your area as well.
Phoenix