Definitely do not store credit card and billing info, use Stripe or Braintree instead. I much prefer Stripe for subscription billing and easy API integration but depending on your app, Braintree could be a better option.
Paypal/Braintree requires that you keep your server PCI 3.0 A-EP compliant (12 requirements) where as Stripe simply requires an SSL and PCI 3.0 A compliance (2 requirements) which is much easier to maintain. So you'll want to keep your compliance overhead costs in mind as well.