Affiliates can be paid on a lead generation basis, and SaaS companies (hosting, cloud storage) work very well with affiliates. The reason they work well is the subscription business model represents for an affiliate continuous cash flow every time there is a renewal. Also, subscriptions ensure a brand gets their money back over time, including what they spent for commissions, and will eventually make a profit.
If you have a good idea for an app, and the skills to create it, then producing your own premium app can be profitable. However, with so many free apps available, it may be hard to convince people to pay. If you want to go down the premium app route, consider having a basic free version to encourage people to download the app in the first place. You can then provide the option of upgrading to a premium plan once users realize how useful the app is.