Ignore the parts about JSON/XML. That's irrelevant.
Problem: you want an RSS reader, but RSS readers are annoying because they are stateful and you have to try to sync them across devices. Or, as in the case of Google Reader they may be discontinued. Best case, you have a dependency on a third party application.
Solution: make a web page on your personal site that aggregates links from your RSS feeds.
This is handy because you can now simply access your own web site as an RSS reader. As a side benefit, you can share this page with your friends to help them find nice links, and help promote stuff that you like to search engines.