The download sizes have been revealed for the two versions of Fire Emblem Fates. According to the checkout page from the Nintendo shopping website, Fire Emblem Fates: Birthright will require 1634 MB of free space. Fire Emblem Fates: Conquest requires slightly less at 1624 MB.
Of course, you can also purchase a physical copy of either game if you don’t have the free space and/or worry about reaching a bandwidth limit. You can preorder the physical releases of the two with the following links on Amazon: Fire Emblem Fates: Birthright and Fire Emblem Fates: Conquest.
In addition to having 1 GB of internal flash memory, a regular 3DS model uses SD cards to store games, saves and other types of data. With the New Nintendo 3DS, Nintendo switched to Micro-SD cards.
For the uninformed, Fates is split into three campaigns: Birthright, Conquest and Revelation. Birthright and Conquest can be bought as separate games as well as discounted DLC packs under specific circumstances (you will need Birthright to purchase the Conquest campaign at a discount and vice versa). Revelation is only available as DLC.
Fire Emblem Fates: Birthright and Fire Emblem Fates: Conquest will be released in the North American region on the 19th of February.