It really helps if you've ran through the game first on Normal. I did that while getting all the collection and 'kill X by Y achievements'. Once you more or less know your way around the game, you can concentrate fully on your Legendary run. It helps a lot to know what weapons you should be scavenging for before any particularly tough fights too. Also if you've completed the Audiophile achievement, you'll have access to the supply caches as The Rookie in any other games you start.
All in all, I've gotta agree with most everyone else. ODST's Legendary isn't as much of a headache as Halo 3's Legendary, partially thanks to the short campaign.