If the question you asked is about local (on client persistence) than your obvious choice is to leverage Ionic Storage as solution. The next question is which “adapter” of Ionic Storage (which is a wrapper around localForage project) to use.
If your app needs to store definitely more than 10-50mb of Data - you probably should rely on sqlite (it is slower than adapters such as indexeddb, but not considerably), which is only available if your project is cordova.
If you need to just cache a few things (even if blobs) until user gets online - I think you can get around with indexeddb (grown in cross browser support recently) or websql (works ok cross modern browsers).