Tidus' weapon is the sword. The weird thing about me and Final Fantasy X is I hardly ever switch out Tidus' weapon. I generally keep the Brotherhood on Tidus throughout most of the game. It works for him, and is especially beneficial after visiting the Farplane, where the weapon gains more abilities. Until I gain his ultimate weapon, I only ever think about switching out the Brotherhood when I want to catch monsters, or when the Brotherhood starts healing water elemental foes, rendering Tidus' attacks useless. Even then, I only use a select few swords.
With equipment customization, Tidus has access to nearly 70 different swords. When you account for the fact that you can attach a number of other abilities to each sword, the weapon possibilities are endless. Here are the swords that I use:
Longsword - This is the weapon that Tidus receives from Auron as a gift from Jecht. It's decent enough, but is easily surpassed by the Brotherhood, which you get very soon after. I only use at out of necessity until I obtain the Brotherhood. It has no elemental or status effects, but has decent enough strength.
Brotherhood - Tidus receives the Brotherhood as a gift from Wakka. Its strength increases are what make it good for me, as Tidus' sphere grid focuses more on agility, leaving strength a little more lacking. Its Waterstrike ability makes it good against lightning elementals. The weapon is enhanced when Tidus visits the Farplane, and it gains its missing abilities.
Nightbringer - Tidus receives the Nightbringer after defeating Seymour on Mt. Gagazet. It contains the Darkstrike ability which nearly always blinds enemies. I attach the Firststrike ability to it, ensuring Tidus always gets to go first so that he can blind a foe at the beginning of a battle. It is worth equipping to Tidus immediately after he gets it, as he soon fights enemies immune to the Brotherhood's Waterstrike ability.
Taming Sword - I only use this sword to capture monsters. Attaching an ability that can inflict a status ailment on a fiend is beneficial, as you'll want to kill the enemies with Tidus' weapon without the enemy wiping out your party. Sleep or Blind work great. Tidus makes a great candidate for capturing monsters because of his agility, and because he can one-hit-KO many fiends.
Caladbolg - The Caladbolg is Tidus' Celestial Weapon, his ultimate sword. The counter abilities alone make it worth it, but Break Damage Limit allows Tidus to do over 9999 damage, and Triple Overdrive nearly keeps Tidus in Overdrive. Unfortunately, it's a pain in the ass to get. More information on acquiring it is here.