Getting the lengendary weapon for Auron is useful to beat the monsters in Omega Ruins, but if you are struggling badly in Omega Ruins, you should train hard enough in Zanarkand so that every monster in Zanarkand areeasy enough for you to beat it in 5 seconds. Getting no encounter weapons in Omega Ruins is not a bad idea, especially if you want to get the treasures instead of fighting monsters (some treasure chests are traps/monsters and they get on my nerves). Anyway in my opinion, it will be a good idea to train in Zanarkand first, and after that try beat sin asap, then Omega Ruins... (or you can train like crazy in Omega Ruins before fighting sin).
Ultima Weapon is not that hard to beat - I guess it has about 100,000hp? (very random guess), but Omega Weapon has surely more than 300,000hp - good luck on beating that beast guys...