My favorite one is Fire Emblem 7, which is the first Fire Emblem localized for the west (so just known as Fire Emblem (GBA))
Happens to be on the virtual console so it's easy to get nowadays. I have it there and also still have my original copy.
It was a perfect entry into the series thanks to Lyn's story, it had interesting maps without being brutally difficult, very lovable units and enjoyable story, and extra modes including a hard mode that didn't feel like sheer rng bullshit.
Almost forgot they put that on the virtual console. I'll have to try it out at some point, and hope they put the others on there at some point.
Well I wasn't going to say it but…
Fire Emblem 7 is many people's favorite, including mine. It's a combination of nostalgia and the fact that the game feels very balanced without any new, untested mechanics. It's certainly not the most complex game but it does what it attempts very well. Fire Emblem 9: Path of Radiance is another popular one, for GameCube. It stars Ike from Smash Bros. Brawl.
However, if you're coming off of Awakening, FE8: Fire Emblem: Sacred Stones for GBA might be your best bet. It has a world map, potential grinding levels, and branching promotions a lot like Awakening. The potential for grinding also makes it one of the easier games, which, along with the relatively short story, makes it a somewhat controversial entry. Still a perfectly viable jumping off point though.
Somebody has to call it out, minus well admit it myself.
I wish there was a simple and cheap way to get most of these games. As far as I know, the only feasible way I might have is through other means, but I'd prefer to buy and own the games.