Hi eric0668,
There is more about foundations that includes links to many options in the foundation post here.
A bunkie board is generally about 2" high and a low profile foundation is usually in the range of about 5" but other than that they would both work well as long as they met the warranty criteria for your mattress (and you can check with your retailer or with Simmons about this).
I would tend to use the foundation that is recommended by the manufacturer of your mattress or at the very least make sure that your support system (which is the bedframe and foundation/bunkie board) met the warranty criteria. You would probably be best to choose something like the Simmons Low Profile Foundation that is designed to work with your mattress and would have good airflow rather than a flexible box spring. Most good quality foundations (or box springs) shouldn’t make noise (although some lower quality versions can develop squeaking or creaking over time).
If you have a bunkie board or slats that have gaps in the range of 3" it should be fine as long as your bedframe also meets the warranty criteria and has good center support to the floor.
The airflow under the mattress really don’t affect cooling at the sleeping surface but is more to reduce the risk of moisture under the mattress and reduce the risk of mold, mildew, and dust mites.
Phoenix