Hi Be.moody,
I’m not so sure that I would include a Simmons hotel mattress (or any major brand mattress) in the “great quality” or even “good quality” category and I would tend to avoid them (see the guidelines here). Almost all of them use lower quality materials in the comfort layers which would be a weak link in the mattress. There is more about hotel beds in post #3 here and there is more about the most important parts of the “value” of a mattress purchase in post #13 here that can help you make better quality/value choices.
There is more about the different types of support systems that are generally most suitable for different types of mattresses in the foundation post here but a one sided mattress like yours will generally do best with a solid non flexing or semi flex support system (which could be either a foundation on a suitable bedframe or a platform bed) rather than a box spring which has actual springs inside it and is designed to provide more flex under the mattress.
Phoenix