Hi finnaeus and swrstock,
There is more information about the different types of support systems that are generally most suitable for different types of mattresses in post #1 here with a few examples of each of them.
A foam mattress will generally do best with a firm, flat, and evenly supportive surface 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 over time without some of the parts bending, sagging, or breaking over time. The support surface under the mattress also needs to have enough surface area to prevent the foam in the mattress from sagging through any gaps or spaces in the support surface over time. I would also be cautious about any parts, joints, or connections that may develop a tendency to start rubbing against each other and/or squeaking over time that can’t be located and easily tightened (this is a typical complaint with many lower cost foundations and bedframes).
If you are looking at Amazon options I would especially take the time to read the critical reviews which can help identify whether there are any potential issues with the design or construction of the bedframe/foundation.
These two foundations both have flexible slats that are designed to flex under the mattress along with plastic slat holders that can break and I would also be skeptical about their overall strength and durability along with the strength of the metal frame and legs. I would avoid both of these.
This one has non flexing slats that are close enough together that there wouldn’t be an issue with the spaces between them. I suspect that the slats are fairly thin and probably less than 3/4" thick and thinner slats can bend and break more easily. They also appear to be using the same listing to sell at least two different bedframes so one of them may be more durable and sturdy than the other. This one may also have some issues with weaker slats breaking or cracking, plastic slat holders breaking, or the legs bending.
This one has a wire grid surface so the support surface area isn’t as large as the support systems that have slat foundations so there would be some risk of the mattress sagging into the gaps between the wires over time. The distance between the longitudinal wires is also larger than other similar platform bedframes that would provide a more supportive surface and smaller gaps under the mattress. This would be a bigger issue with a latex support core but it could also have some effect on polyfoam support cores over time as well. Given the price it’s also not surprising that there are a fairly large number of critical reviews that talk about the frame or legs bending and that indicate that the quality and strength of the steel and the foundation itself isn’t as high as it could be and there are also a percentage of them that appear to develop squeaking issues over time that may be difficult to locate and solve.
My comments here would be similar to the comments about the Euro Smart platform bedframe that you linked that has non flexing slats. The distance between the slats appears to be suitable for a foam mattress and it has a center beam that is supported to the floor. This one doesn’t have plastic slat attachments that could be subject to breaking and they rest on the side rails and center support beam.
While none of these are in a budget range that it would be reasonable to expect that you are purchasing a high quality support system so there will be some “luck of the draw” involved … out of the ones you linked I would probably lean towards the Deluxe Faux Leather Platform Bed or alternatively the Euro Smart Base/Wooden Slats Mattress Foundation.