I don't really know Earthbound/Mother at all, but Fire Emblem is my favourite game franchise, so I'd be happy to help give you more information.
Fire Emblem's been going on for a long time, starting with the first game back on the NES. It wasn't until the 7th game in the series that FE started to be released outside of Japan, but since then almost all games have gotten international releases (with the exception of 12, a remake of 3, that was not brought out of Japan). Almost all of the games have their own story unconnected to other games in the series, which makes them easy to pick up and playing. Of the English released games, 10 is a direct sequel to 9, but even then, it can be played and enjoyed on its own and fully understood without playing the original.
Some of the older games can be difficult to find now, but I would suggest the most recent game,
Fire Emblem: Awakening, as the best place to start. The story of FE:A follows Chrom, a prince of the country Ylisse, as he works with his tactician (a player avatar character with a default name of Robin) and small army of soldiers known as the Shepherds to protect his country from the threat of a war-mongering king from a neighboring country. As the game progresses, Chrom, Robin, and the Shepherds find themselves embroiled in an even deeper struggle than they imagined, and find themselves in a fight for the future of the world. As the most recent game, it is the easiest to acquire (still available in stores or can be downloaded directly from the e-shop to your 3DS), and also is the most player-friendly in terms of GUI, options, various difficulties, etc.
Where the game really shines is its characters and gameplay mechanics. You start will a small group and recruit more playable characters as you progress. Characters each have different strengths and weaknesses in battle, and can also talk to each other, form bonds, and even get married in some cases. The large cast gives you plenty of options for which characters you'd like to train and use in battle or for different circumstances, and also offers a strong replay value by playing the game over again on different difficulties while using different characters.
The basic gameplay is that of a turn-based strategy RPG. Each chapter is a single battle, and your characters must attack and defend against enemies to achieve a goal, usually killing the enemy commander or clearing an area of enemies. Different characters use a wide variety of weapons (various melee weapons such as swords, lances, and axes; ranged weapons like bows, and different forms of magic), and some characters even transform and attack in battle (such as Nowi, a character who appears to be a young girl but can transform into a powerful dragon and blast people with dragon fire). Some characters fight on foot, others right horses, pegusi, or wyverns. Characters also learn Skills that can give them an advantage in combat. Taking the role of a strategist, it is your responsibility to tell which units to do what to enable a victorious outcome.
Other games all have similarities in terms of base plot and gameplay. The MC is almost always a member of royalty who is in charge of a small army or group of soldiers that is fighting for a goal, recruiting new playable characters along the way, and eventually leading to a big showdown with the ultimate boss. The games' worlds are pretty much exclusively based on generic western fantasy style words, with armor and swords and magic and dragons, though each world has its own unique bits as well. The core gameplay is the same throughout the series, though some games feature new or different mechanics or changes that may be unique to that particular game.
If you play and enjoy FE:A, some of the other games in the series can be acquired, some easily, some with more difficulty. FE7 (known only as
Fire Emblem outside of Japan) and
The Sacred Stones (FE8) were originally GBA games but can be download on the WiiU virtual console.
Path of Radiance (FE9, GameCube),
Radiant Dawn (FE10, Wii), and
Shadow Dragon (FE11, DS) can be acquired through old- and used-game resellers, but may be expensive due to low print runs and age. The next game in the series,
Fire Emblem if, will be coming out for the 3DS sometime in 2016.
If you'd like more information on Fire Emblem, we actually have a
thread dedicated to the series right here on PokéBeach.