Hi Jalan,
There is more information about support systems (bedframes and foundations or platform beds) that are generally suitable for different types of mattresses and some examples of each of them in post #1 here.
Which type of support system would be “best” will depend on the specifics of the mattress but a mattress with a polyfoam support core will generally do best with a firm, flat, and evenly supportive support surface underneath it that has minimal to no flex under the mattress and for larger sizes with at least one center support beam that has good support to the floor to prevent any sagging in the middle of the mattress. The components need to be strong and durable enough to support the weight of the mattress and the people sleeping on it without any of the parts of the support system bending, sagging, or breaking over time. The support surface under the mattress should also have enough surface area to prevent the mattress from sagging through any gaps or spaces in the support surface over time but still allow some airflow under the mattress. I would suggest that the gaps between the slats are no more than about 5" (with 1 x 3 slats) although less than 4" would be better yet. Stiffer, stronger, and less flexible wood with a higher bending strength would also be better than softer or more flexible wood with a lower bending strength (see here).
If your mattress has a latex support core then I would look for gaps that are less than 3" between the slats.
The simplest way to choose a foundation would be to use the recommendations of the manufacturer or retailer that is selling the mattress you are purchasing but if you decide to do any additional research then I would also make sure that your support system meets the warranty criteria for your mattress as well because different manufacturers can have different criteria or exclusions for their warranty.
Phoenix