This digital camera supports an SD|SDHC|SDXC compatible memory cards, which is typical of many cameras of this spec and age. SD cards are by far the most common type of memory card. They are compatible with the majority of digital cameras.
It may also be worth also looking at one of the alternative cameras that support an SD|SDHC|SDXC memory currently available including because of it's better review score, the Rollei PowerFlex 800[plb_1950271_price], the Fujifilm X10[plb_1150_price], or the Canon IXUS 155[plb_2176423_price].
If the memory card type of this Fujifilm digital camera is not good enough for you then you might want to consider the Sony DSC-W570[plb_2128686_price] (MS Duo|MS PRO Duo|MS PRO Duo HS|MS Pro-HG Duo|SD|SDHC|SDXC and higher rated).