If you're new to Custom Deliveries, then one thing to be aware of is that the weekly rewards and scrips earned for every Custom Delivery — regardless of expansion, difficulty, etc — is the same. So once Dawntrail Custom Deliveries are released, they'll be giving the exact same weekly exp and scrips you could get from the Heavensward Custom Deliveries, etc. Which is to say: do all of the Custom Deliveries that already exist, they're no less valuable than the newest ones that will arrive later!

The only difference for weekly rewards is that for Custom Delivery NPC's whose quest chains you've finished, they'll sometimes want certain turn-ins that are considered special and give boosted rewards. But you won't have to worry about that for a handful of weeks if you're just getting started.