I use Cloud as my punching bag. His attacks are so slow that they're easy to dodge and punish with someone like Zidane or Tidus (note that I have Sneak Attack equipped in the video). Remember that there is an AP Chance (Deal over/under X amount of damage, HP attack first, etc.) for every battle, so you can also master abilities relatively quickly.
I'm not sure about Spirit Stones specifically, but to get most of the weapon Trade Items you'll need some sort of Elixir from the Duel Colosseum.
Once you've gotten the proper Elixir for the Spirit Stone, it should appear in the Shop. Therefore it'd be best to just get one of each Elixir (excluding Megalixir, the Lv 120 CPUs aren't worth it).
You get Dusty Elixir from the first (easiest) course, Elixirs from the second, Hi-Elixirs from the third, and Megalixir from the last. The last two Duel Colosseum modes have to be bought in the PP Catalog (it's Lunar Whale and something else).