Excepting the Satellaview game and the remake of Monsho no Nazo for the DS, I've played through every game up through Awakening. I have Fates and Echoes, but Echoes has faggotry and Fates never held my interest.
As for the TRPG gameplay, it varies with each entry. Earlier titles rely more on strategy and tactics, and Thracia 776 is especially brutal in this regard. Gaiden and Sacred Stones allow for grinding and are fundamentally different than all other games in the series before Awakening. If you need a game with which to start, do the seventh game, the one for the GBA (the first release outside Japan). I've also heard that Tear Ring Saga is a good primer as well.
@noyoushutthefuckupdad I have a strong distaste for FFT/Ogre Battle style TRPGs. They're basically RPGs on a grid while Fire Emblem relies more on strategy and grew naturally out of Intelligent Systems Wars series. The stats and calculations are much simpler in FE than in games like FFT, Ogre, Battle, Disgaea, etc. where the direction a character is facing makes a difference in how much damage they do or receive and battles play out at a snails pace. FE's pedigree can be traced back to Shougi while other TRPGs are something else entirely.