You’ll find some gear that gives reputation bonuses for certain modes, such as crucible, vanguard, and iron banner. Iron banner, for example, has shaders, emblems, and class armor. Once you get emblem/shader for one character, you can go to kiosk in north tower to retrieve, for free, with your other characters.
Iron banner, and other special events like Crimson doubles are worth doing. For example, in iron banner, once you hit rank 5, 310-320 gear can drop.
Also, once you hit rank 5 with a character, complete each bounty daily, but don’t turn them in. Next time iron banner rolls around, you can turn them in to level quickly (be sure to equip your iron banner gear (class armor, shader, emblem which give bonus iron banner rep). Additionally, once one character hits rank 5, your other characters will level faster. Here’s a guide to leveling in iron banner: https://www.reddit.com/r/DestinyTheGame/comments/3t5als/the_full_iron_banner_guide_to_ranking_up_fast_now/