When Edgar first joins your party, he is most likely the strongest character and is much helpful with his assortment of tools. A highly useful one is the Auto Crossbow, which can be bought inside the chambers of Figaro Castle. It will be your first weapon to hit multiple targets, and does significant damage early on in the game.

The "ultimate" tool can be considered the Air Anchor, which is located in the Fanatics Tower during the World of Ruin. Simply go to the first treasure room, and hit the hidden switch to the right of the treasure chest. Then go back outside and you'll find a door below you. The Air Anchor is inside.

Every other tool can be purchased at Figaro Castle, in which you also get a 50% discount if Edgar is in your party. The only exception is the Chain Saw, which is found in the town of Zozo. Want a hint? 6:10:50...

Notes for the Colosseum: you can win the Air Anchor if you bet the Cursed Ring or the Genji Armor. However, should you bet the Air Anchor itself and win against Brontaur, you receive a Zephyr Cape. Yeehaw.