Opt for a soft mattress and sleep without a pillow. Because you aren't likely to change your sleeping habits all at once, if at all, arch your back less by keeping your head level with the rest of your body. You need a mattress that is soft enough to be comfortable without a pillow in this case.
Choose a mattress that isn't too firm. An overly firm mattress may support back and side sleepers well, but doesn't have enough give for stomach sleepers.
Pick a mattress that isn't too soft either. A mattress that gives too much arches the spine even more than stomach sleeping already does.
Cater to both people sleeping on the bed by choosing a mattress with adjustable firmness. Retailers such as Select Comfort offer the option of one or two air cushions in these types of beds (see Resources). Having two air cushions means you can each have a firmness setting to suit your individual needs.