I can't remember the FF6 first boss. All I can remember is that dayum Ultros. Funniest boss I ever had encountered that far.
The first bosses of FFIV (Mist Dragon), FFV (Wing Raptor), FFVI (Whelk/Ymir), and FFVII (Guard Scorpion) are functionally the same "don't attack when it does the thing." Personally, I can't stand them just because I think it was laziness to make the first boss effectively the same FOUR GAMES IN A ROW, but I do believe that it was a pretty good idea in 1991.
I think a good first boss(TM) drives home the importance of the core mechanics of the game that were hopefully introduced in the first dungeon(TM). Two examples:
Looking more recently (in comparison), I thought Forneus, the first boss of Shin Megami Tensei: Nocturne, was really good, considering the area where he appears has a relatively strong demon who uses the element he's weak against (and a save point right next to his room (which turns out to be a relatively rare occurrence in that game). He teaches the player that this elemental thing is REALLY IMPORTANT and you will not survive if you don't take advantage of it, just as Matador, an infamous early boss, teaches the player that stat buffs and debuffs can mean the difference between life and death.
Even more recently and only tangentially a "classic" JRPG, I just got into Dark Souls (which is more of a wrpg but it's from a japanese company) where the first two bosses' attacks have big, obvious blind spots but otherwise do huge damage and you have the opportunity to do plunging attacks from high ground, but if you linger too long they will wreck you before you get a chance. They really introduce the core concept of most boss fights in the game: they will give you the tools you need to beat them if you pay attention but will punish you if you don't use those tools effectively or if you thing that using those tools means you can let your guard down.