Due to the firm nature of a slatted bed frame, the ideal mattress for a slat bed would also be firm, but with some "give" to it as well, since the frame will not have any "give" at all. Mattresses that fit this description include memory foam and an inner-spring mattress.
Where some bed frames allow for some movement under the weight of the body, slat beds do not. Because of this, a mattress that simply functions as a cushion, like a futon mattress, may not offer enough back support for comfortable long-term use. However, such a mattress might be ideal for temporary use, such as on a guest bed. An air mattress might also be a good option for more transient use.
Every person is different. Needs for back and neck support vary from person to person, as do personal comfort preferences. For this reason, finding the right mattress is ultimately a personal decision and should not be made without the opportunity to actually feel the difference between selections.