What type of catch up mechanics, off hand? Just curious because I might start running my mage/dru/pal up
As Chris said, it is renown related. New characters will get the standard 3 ways (collect souls, 1000 anima, & weekly Cov quests) to upgrade their renown for the week, but they will also be able to get renown from a plethora of other sources until they are caught up with everyone else.
Catch-up renown will come from the daily emissary quests, dungeon drops, raid drops (including LFR), and probably other place (like maybe the Maw and Torgast). Renown 10 also bumps up the item level of world quests and drops from "rare" bosses.
I haven't spent much time gearing alts, but I think the cheapest way to get over 155, is to get renown levels through the easy solo things. Then run all the covenant quests to get the gear. Spend anima to upgrade the gear, and then go kill "rares" in the world to fill in low slots. The next day (if you have increased your average ilevel enough), you go kill rares again, and get higher ilevels of those same items.
Outside of maybe the table, the Anima buildings feel underwhelming/worthless, so spending anima on gear probably wont matter.