Update 22 introduces 3 reputation factions: Men of Dale, Elves of Felegoth, and Dwarves of Erebor. Quests in the different areas reward reputation with a particular faction.
Each faction has a reputation barterer for a particular kind of gear: Men of Dale, Light; Elves of Felegoth, Medium; and Dwarves of Erebor, Heavy. You barter using the Tokens of the Lake and Rivers, which are earned by doing quests for any of the factions. However, to barter for the gear, you will need to get particular rep standing with the appropriate faction for your class. New jewellery is item level 345 incomparable/teal and rare/purple. New armour is item level 340 incomparable/teal and rare/purple.
You may want to start with quests for the faction that has the gear you want. If you have marks and medallions or LOTRO Points to spend, you may want to invest in rep accelerators. At this point, I don't know how hard it will be to reach kindred for any faction.
Different Task Items reward reputation with a particular faction, although all Task Bulletin Boards in the area off the same items. Deadly Claws and Shiny Carapaces for Men of Dale; Bristled Fur and Petrified Branches for Elves of Felegoth; and Rusted Scimitars for Dwarves of Erebor.