I would disagree a bit on advance wars. It's true that they're by the same developer IIRC, and they're both turn based strategy with similar movement/attacking systems.
However, Fire Emblem you have units that improve over the game and are gone for good if they're lost. You also only get a set number of units in a senario. In Advance wars, you capture areas to increase your production, and make new units. This is a very significant difference, as far as I am concerned. For me, AW always came to grinding down the oponent....I'd almost have them, they'd use their CO powers, and come back a bit. Never enough where I didn't know I was going to win, but enough to delay it for a number of turns. Many battles took forever, and were not fun, IMHO. On the other hand, FE, I keep replaying battles so I don't miss/lose a character.
I have only played the original Advance Wars, and Fire Emblem: The Sacred Stones. I traded AW away, and didn't bother getting any others. I have gotten all the Fire emblems available in North America.
My suggestions, though I haven't played many of these, with the top most being closest to FE, AFIK.
-Final Fantasy Tactics (PS1, PSP, GBA, DS) -- SRPGs, with fantasy worlds
-Disgaea (PS2, PS3?, DS) -- SRPGs with fantasy worlds
-Advance Wars (GBA, DS) -- TBS, with modern settings
-Front Mission (PS2, DS, others?) -- TBS with futureistic settings (Mechs
)
And just to be sure you haven't missed any Fire Emblem games for the kids, there are four in NA. Fire Emblem(GBA), Fire Emblem The Sacred Stones (GBA), Fire Emblem Path of Radiance (GC) and Fire Emblem Radient Dawn (Wii)
GOod luck!