Oh, I'm glad Fire Emblem was mentioned. But then again, it has gained popularity since FE7.(Hmm... used to know what were their subtitles). Since I am dormant fan of the series I think I can draw you a better picture.
Anyway, Fire Emblem was kinda my intro to strategy games back then; meaning I totally sucked at them at the time I was playing FE3-5. I don't have a GameCube so I missed out on the recent ones and I've played the three GBA ones. They weren't bad but I really had a heart for the old one; actually, I kinda have a heart for old games. Gameplay was a larger factor than graphic back then... I think. I digress, the new ones were too... linear, except FE8... or 9, I forget. The ones with two heroes, that was sort of fun. I didn't get to replay any of the GBA ones since they seemed dragging for me. I did play FE4 and 5 a couple of times, despite not finishing 5.
Sorry... I don't remember FE3 too well... except that the first half of it was a remake of 1, and the second part was the actually FE3. That one was quite long.... A bit linear, but then again I can't really remember.
FE4 was probably the easiest. But the fact that you can pair up your units and control their offspring in the second half of the game just makes it so damn fun. I wished they bring back the 2 generation system... I liked it.
I liked FE5... sort of. Nintendo probably thought that the previous one was too easy and decided to up the difficulty... a lot. Though FE5 had the best systems in the series. No shop, you'd have to capture an enemy unit and sack their stuff to keep your army geared. And the weapon triangle system there was toned down so much that it could be ignored for the most part; since you do hate weakness systems. It had some branching paths but not very many and some mission involved not just kill all opponents or killing the boss. For me(at that time), there was much to explore in FE5. The game was very enjoyable... too bad I didn't get to finish it. Haha, got stuck then my computer broke along with my saves. I haven't gotten to playing them again but I will someday, I think I'm better at strategy games now.
Although, without guides and/or translation, you'd miss out on a lot and believe me FE has a LOT of missable stuff/characters/etc. I'd say play the GBA ones and if you enjoy them, play the ones in SNES. I can dig into my back ups if you want. I think I have an old translation of FE4.
EDIT: Sorry that thing about NO SHOP in FE5, that was an exaggeration. There were shops, but in every 5 or so chapter so they were very limited.