I always loved Cloud's Organics sword. It was my favorite the first time I played through, and it's still one of my favorite weapons in the series.
Tidus's Brotherhood also has an amazing design. Water is my thing, so a water sword is the thing for me.
I tend to play the white mage role in games, so I'd probably pick one of Yuna's staves. (I particularly like the green and blue swirly one.)
I would dual wield knives and the main one would be the chicken knife from ff5 and the other one I would alternate between mage masher and dancing dagger of course theres other knifes I like but can't remember the names of them
I would probably use the Yuffie/Cissnei weapon I like the idea of it striking the target and then returning to you, although I would definitely want a close range weapon on the off chance it got stuck or something.
And the obvious choice to me is the Squall/Lightning gunblade. You can attack up close with the blade or from a safe distance with the gun part therefore I'm completely sold. From a practical standpoint I think its the best. Though I also just really like Yuffie and Cissnei's weapon of choice.