Dear Jony, er I mean, Jonny,
App purchases are associated with your entire account, not just the device they are bought on. Once you have authorized yourself with that account, you can re-download your software at no cost on other devices.
You can also transfer purchases from your device to your home computer and then sync them around as needed. Right-click your device in the iTunes sources list and choose Transfer Purchases from the contextual pop-up menu.
Transferring your purchases adds them to your main iTunes library, even when they were bought on-device through the iOS App Store.
As for in-app purchases, it depends. Non-consumable purchases, i.e. buy once, use-forever purchases are good for all devices registered to an account. Examples of nonconsumable purchases include adding game levels, enabling ad-removal, and unlocking features. Once unlocked, they remain available for all devices. Application developers are able to check for prior purchase and apply that purchase to new devices through a process known as restoring purchases.
For subscriptions and replenishable items, otherwise known as "consumable" purchases cannot be shared across devices. Typical consumables include monthly subscriptions, extra ammo or food, or other items that are used up over time and must be re-purchased to access more of the same. This morning, Uncle Rich pointed out this Apple knowledge base article on the matter.
So other than consumables, your bases are covered. With subscriptions and similar items, be aware they are one-device-only choices by default (although clever developers can sometimes find ways to work around that.)
Love & kissies,