Jtat84,
A solid platform that has good center support to the floor will be fine for most mattresses (but always check with the manufacturer to make sure your support system is suitable) and the only reason to add a separate foundation would be to add height to your sleeping surface. A solid platform doesn’t breathe under your mattress so if you are in a humid area or there are other risk factors that could affect the risk of mold or mildew then it may be worthwhile adding a bed rug on top of the platform (see post #10 here).
There are some two sided mattresses that would be fine on a solid platform so I would go by the manufacturers recommendations for a support surface. If you really like a two sided mattress that requires a box spring (with springs) then you can always use the box spring on top of the platform although it would raise the height of your sleeping surface.
There is more about dust mite allergies in post #2 here and about different types of mattress encasements (some are more breathable than others) in post #2 here. An allergy encasement will work equally well on any mattress that it fits.
No … a mattress pad is most suitable if you need to do some “fine tuning” to the comfort of your mattress. If the mattress by itself is a suitable choice for you then you won’t need one … only a mattress protector that is thinner and will have less effect on the “feel” of the mattress. If the mattress encasement you are using is waterproof then you won’t need a mattress protector but a non waterproof and more breathable encasement (for dust mites and allergens) with a fitted sheet style protector (for protection against body fluids, spills, and accidents) that can be more easily removed and cleaned is a good combination. There is more about the pros and cons of the different types of mattress protectors in post #89 here.
Every type of mattress will have higher quality and more durable versions and lower quality and less durable versions and I would treat the choice of materials or the type of mattress as strictly a preference issue not a “better/worse” issue. No matter what type of mattress you tend to prefer I would always make sure that it uses high quality and durable materials. There is more about the most important parts of the “value” of a mattress purchase in post #13 here but choosing the “best” mattress for you comes down to testing for suitability (hopefully using the testing guidelines in the tutorial) or what I call PPP (Posture and alignment, Pressure relief, and Personal preferences), checking the materials inside your mattress to make sure that there are no lower quality materials or “weak links” (see this article), and then comparing your finalists for value based on all the parts of your personal value equation that are most important to you.
While I can certainly help to narrow things down and help with “how” to choose and what to avoid … I don’t make specific suggestions or recommendations for either a mattress, manufacturers/retailers, or materials because only you can feel what you feel on a mattress and there are too many unknowns, variables, and personal preferences involved for anyone to know which type of mattress design or materials would be best for you based on specs (either yours or a mattress) or theory at a distance (see mattress firmness/comfort levels in post #2 here).
Phoenix