If Path of Radiance and Radiant Dawn weren't so expensive and hard to come by, I would recommend those like the person above. That being the case, they're not what you should seek out to start with. There's no sense in spending upwards of $60 on something you don't know whether you'll even like.
When it comes to these threads popping up asking about which games to start with, I tend to stick with recommending Fire Emblem and Fire Emblem: The Sacred Stones. Both can be found on the Wii U eShop, and they're Game Boy Advance Virtual Console games. They're both $7.99 (or whatever your equivalent to that is if you live outside the US).
The game I listed simply as Fire Emblem is alternatively known as Fire Emblem: Rekka no Ken/Fire Emblem: Blazing Sword, or Fire Emblem 7. As you can guess, it's the 7th game in the series, but it was the first game in the series released outside of Japan, thus why it's known simply as Fire Emblem. Being the first international release for the series, it includes tutorials that will help you to understand the gameplay mechanics. It also has a pretty good story, something which Awakening and the Fates games lack.
Somewhat similar to the Fates games, FE 7 has different paths depending on which Lord you pick. The main path follows Eliwood as the main lord and is a bit easier. Another path features Hector as the main lord and is a bit more challenging than Eliwood's path.
Meanwhile, Fire Emblem: The Sacred Stones is one of the easiest games in the series and probably held that title until Awakening. It is similar to Awakening in that you walk around a map and occasionally battle monsters to grind up levels. (Meanwhile, in the other games, instead of traversing a map you simply end up in the next location by story progression. You can grind in some of those games, but not all of them, and do so in a designated building called the Arena.) Due to its simplicity compared to the rest of the games and its price point, it's hard to not recommend to a newcomer.
I can't in good conscience recommend Awakening or Fates as part of what I like about this series is the characters and stories in the games. Actual decent storytelling took a backseat to time travel, husbandos, waifus, and nonsensical children from the future. I doubly cannot recommend them as the map design in Awakening is atrocious by series standards and, while Conquest brings back some challenge, Fates overall changed numerous gameplay mechanics that were part of the series for 25 years. If the only thing that interests you is the whole waifu thing, it shouldn't be hard to find much better elsewhere.
Given the dates of your posts, at this point you've probably already purchased Birthright. Nonetheless, I highly recommend the older installments in the series because they're far more interesting tactics games. If nothing else, Fire Emblem and Fire Emblem: The Sacred Stones would serve as good bridges for you to make your transition into the older games as simple as possible.
Finally, as someone who started with the older games, don't let all the talk of the difficulty of the older games scare you off outright. This is overblown, especially by people who have never actually bothered to play the older games and who probably aren't suited to strategy games in the first place. You can jump into nearly any of the games and get the hang of it.
If only it was possible to marry Tibarn in the older games. He's my fave! <3 Anyway, hope you end up enjoying FE! 
