bed slats ... or NOT
Bed slats are meant to support a box spring which has it's own internal frame. If you aren't using a box spring then you can just use plywood. A firm support is better than a spongy one, in my opinion. The memory foam mattresses are about 10" thick and heavy as a horse. Mine just sits on a box spring, also about 10" thick right on the floor, no frames or head boards to get hurt by climbing in and out. You can sit on the edge on any place you want, the side or the end, what ever.
There are so many types of mattresses now, that you really have to design the support based on which mattress you will be using.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)