Any card that can work in SPI mode (backwards compatible MMC mode) - which rarely stated on the card - but generally most cards do. All SD should - SDHC/SDXC don't have to but more often than not seem to.
Memory size support would be a function of the library you are using - I imagine most support up to 32gb minimum.
Speed doesn't play much of a role since we are using the SPI protocol to access them