Pick a futon mattress that fits the frame you have. Futons come in the same standard sizes as traditional bed, including twin, full, queen and king. There are also futon-specific sizes, such as full loveseat, queen loveseat and ottoman. Whatever size frame you have, that's the size mattress you should pick.
Choose a thicker futon mattress if you plan to use it primarily as a bed rather than a couch. The thicker mattress will help support you while you sleep, and will hold up better over time. A 100-percent cotton futon mattress tends to be the thickest option.
Find a futon mattress that has more flexibility if you plan to use it primarily as a couch, or if you plan to use it as a bed and a couch. Polyester and cotton blend mattresses tend to be the most flexible, but a foam futon mattress can work in this situation as well.
Pick an innerspring futon mattress if you want your futon to feel more like a traditional couch or bed. This type of mattress has an innerspring construction, and is heavier than most futon mattresses. It can also be more expensive.