One character will always specialize in swords since they are the best weapon in the game (hello blood swords). The other two characters will end up with different weapons since swords are already taken. The best thing to do is just to leave the main characters with their default weapon types since axes are alright and bows will eventually come in elemental flavors (just around the same time as those Flan type enemies show up).
Also enemy AI is set up so that they will attack the softest target first and foremost. I had Firoin with a shield and Maria in the back with a bow which left Gus with his hand-me-down armor (you seriously don't really need to buy anything until you get to the dreadnought aside from a life spell scroll) to take all the damage and end up with over 3000 hp by Mystida whereas Firoin had 700 hp and Maria had 400 hp (and yes with this build I had Maria as my dedicated Black Magic user and the other two subbing White and Support magics).
From what I remember though you still stat-up pretty quickly when you switch regions
That was the crux of my last post. The only time that this isn't true is before Kas'on when the changes between regional enemies is so insignificant that the characters won't gain that much in stats. The only reason why that isn't apparent until later is due to how low your initial stats are and how small the increments really are.
When I first played FF2 I did what everyone else did and spent hours grinding in the beginning areas by whacking myself until I thought I was strong enough to take on the next area. I stopped that run around Deist when I was getting my ass kicked all over the place and like so many other files at the time the run vanished into the aether. At the end of 08 I decided to try again but without the excessive grinding or any grinding at all and I made it all the way past mystida before getting sidetracked by a PS2, 10 games that I could finally play that I couldn't before, plus 30 others all within the space of a month, and then finally getting challenged to a playthru of Beyond the Beyond (also school and an impending time limit) (also also about 50 other games sitting in my backlog while I'm thinking about it).