Tweak, did you try to play FFII Jap or FFIV Jap/FFII Eng? In FF2 Eng you start on an airship playing as Cecil and fight a couple monsters before going back home, then the real game starts. FF2 Eng is definitely worth playing if you can forgive the outdated graphics. It was the best in the series in lots of people's opinions.
So was the game any good? I've only played FF Tactics, VII, VIII, IX, X, XI and XIII... And out of those I only liked 3 of them (VII, IX, and XI). I tried tossing on II (I think? It started on a ship and then they talked about a crystal) the other day but it looked really outdated at this point like it would be a cheesy story.
I then tossed on Chrono Trigger and played it for a good hour. That game is timeless!
US FFII you mentioned is actually FF4 and is the best in the series for pure story telling. That game set the gold standard for Shakespeare tragedy JRPG story telling.
Try again. If you can't stomach the dating, thete is a more modern 3D remake on DS that is true to the original in every way. (Square didn't do it, Matrix did, so its true and NOT turned into 10 hrs of FMV with guns and splosions)
That out of the way, the III I'm playing is a similar 3D remake and is the real III, as in the last one on NES before IV that you played (US SNES FFII).
It shows its 8 bit heritage and lack of cart ROM space for extensive text and story but its still an amazing game by NES standards. Its the only official release of the NES Japanese FFIII in the US.
Keep in mind that Final Fantasy IV on the DS is the 3D remake not the original sprite-based game. You can also get that 3D remake for iOS (that's what I've been playing it on). Also, if you own a PSP or a Vita, you can get Final Fantasy IV The Complete Collection, which includes Final Fantasy IV (2D remastered sprites), Final Fantasy IV Interlude and Final Fantasy IV The After Years.
So is III. It's also on Android, I have it on my tablet. The FF1 remake isn't too bad, (not as good as the III/IV renake) but not old blocky chars either.