Hi buckeye_614,
The first place to start your research is the tutorial post here which has all the basic information, steps, and guidelines that will help you make the best possible choices … and avoid the worst ones such as chain stores and major brands.
mLily is a Chinese manufacturer that makes some good quality and value memory foam mattresses and are CertiPur certified (see the memory foam guidelines I would suggest in post #10 here) but like any mattress purchase I would make sure that in addition to testing a mattress for PPP that you also know the specifics of every layer in the mattress so you can identify any weak links in the mattress and make more meaningful comparisons between mattresses.
I would make sure that it has a center rail with good center support to the floor but other than this it would depend on the mattress. For most foam mattresses it would be fine without a foundation. With a mattress that had a latex support core I would make sure that the distance between the slats was no more than 3" in which case it would also be fine. With an innerspring mattress I would check with the manufacturer or retailer of the mattress to make sure that a slatted foundation / platform bed was suitable for your mattress and met the warranty criteria.
Once you get to step 3 in the tutorial post … some of the better options and possibilities I’m aware of in the Houston area are listed in post #2 here.
Phoenix